Abstract
The origin of the theory of bendings as one of the basic problems of metrical geometry is associated with the names of Euler, Lagrange, Legendre, Cauchy and Gauss. After it was discovered that on surfaces there is an “intrinsic geometry” that does not depend on the external form of the surface, there naturally arose the question of the possibility of deforming the surface, preserving its intrinsic geometry. Consideration of isometric immersions (or, as we say, realizations) of abstractly given Riemannian metrics also leads to the problem of bendings of surfaces as to some problem about the uniqueness or non-uniqueness of an immersion.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aleksandrov, A.D. (1937): Infinitesimal bendings of nonregular surfaces. Mat. Sb., Nov. Ser. 1, 307–322 (Russian), Zbl.14,413
Aleksandrov, A.D. (1938): On a class of closed surfaces. Mat. Sb., Nov. Ser. 4, 69–77 (Russian), Zbl.20,261
Aleksandrov, A.D. (1948): The Intrinsic Geometry of Convex Surfaces. Gostekhizdat, Moscow. German transi: Die Innere Geometrie der Konvexen Flächen. Akademie-Verlag, Berlin, 1955, Zbl.38,352
Aleksandrov, A.D. (1950): Convex Polyhedra. Gostekhizdat, Moscow. German transi.: Konvexe Polyeder. Akademie-Verlag, Berlin, 1958, Zbl.41,509
Aleksandrov, A.D. and Vladimirova, S.M. (1962): Bending of a polyhedron with rigid faces. Vestn. Leningr. Univ. 17, No. 13 (Ser. Mat. Mekh. Astron. No. 3), 138–141 (Russian), Zbl.135,407
Aleksandrov, V.A. (1989): Remarks on a conjecture of Sabitov on the rigidity of the volume under an infinitesimal bending of a surface. Sib. Mat. Zh. 30, No. 5, 16–24. Engl, transi: Sib. Math. J. 30, No. 5, 678–684 (1989), Zbl.687.53007
Artin, M. (1968): On the solutions of analytic equations. Invent. Math. 5, 277–291, Zbl.172,53
Artin, M. (1969): Algebraic approximation of structures over complete local rings. Inst. Hautes Etud. Sci., Publ Math. 36, 23–58, Zbl.181,488
Belousova, V.P. (1961); Infinitesimal deformations of surfaces. Vestn. Kiev. Univ. Ser. Mat. Mekh., 4, 49–57 (Ukrainian).
Berger, E., Bryant, R., Griffiths, P. (1981): Some isometric embedding and rigidity results for Riemannian manifolds. Proc. Natl. Acad. Sei. USA 78, 4657–4660, Zbl.468.53040
Berger, M. (1977): Géométrie. Vols. 1–5. Cedic, Paris, Zbl.423.51001
Berri, R.Ya. (1952): An integral invariant of binary forms of the fourth degree. Usp. Mat. Nauk 7, No. 3, 125–130 (Russian), Zbl.49,153
Bol, G. (1955): Projektive und affinen Eigenschaften des Darbouxschen Flächenkranzes, Abh. Math. Semin. Univ. Hamburg 20, 64–96, Zbl.65,145
Borisov, Yu.F. (1965): C1, isometric immersions of Riemannian spaces. Dokl Akad. Nauk SSSR 163, 11–13. Engl, transi: Sov. Math. Dokl 6, 869–871 (1965), Zbl.135,403
Boudet, R. (1961): Sur quelques propriétés géométriques des transformations infinitésimales des surfaces. Thesis. Fac. Sci. Univ. Aix-Marseille, 78 pp.
Bricard, R. (1897): Mémoire sur la théorie de l’octaèdre articulé. J. Math. Pures Appl. 5, 113–148, Jbuch 28, 624
Burago, Yu.D., Zalgaller, V.A. (1960): Polyhedral embedding of a development Vestn. Leningr. Univ. 15, No. 7, 66–80 (Russian), Zbl.98,354
Bushmelev A.V., Sabitov, I.Kh. (1990): Configuration spaces of Bricard octahedra. Ukr. Geom. Sb. 33, 36–41 (Russian)
Calabi, E., Hartman, P. (1970): On the smoothness of isometries. Duke Math. J. 37, 741–751, Zbl.203,543
Chern, S.S., Osserman, R. (1981): Remarks on the Riemannian metric of a minimal submanifold. Lect. Notes Math. 894, 49–90, Zbl.477.53056
Cohn-Vossen, S.E. (1929): Unstarre geschlossene Flächen. Math. Ann. 102, 10–29, Jbuch 55,1016
Cohn-Vossen, S.E. (1936): Bendability of surfaces in the large. Usp. Mat. Nauk 1, 33–76. Zbl.16,225 (Reprinted in the book: Cohn-Vossen, S.E., Some questions of differential geometry in the large. Fizmatgiz, Moscow, 1954 (Russian))
Connelly, R. (1974): An attack on rigidity. I, II. Preprint, Cornell Univ., appeared in: Bull. Am. Math. Soc. 81, 566–569 (1975), Zbl.315.50003
Connelly, R. (1978): A flexible sphere. Math. Intell. 1, 130–131, Zbl.404.57018 Connelly, R. (1980): The rigidity of certain cabled frameworks and the second order rigidity of arbitrarily triangulated convex surfaces. Adv. Math. 37, 272–299, Zbl.446.51012
Connelly, R. (1992): Rigidity, in: Handbook of convex geometry (P. Gruber and J. Wills, eds.) (to appear)
Darboux, G. (1896): Léçons sur la théorie générale des surfaces. Part 4, 2nd. ed. Gauthier-Villars, Paris, Jbuch 25,1159
Dorfman, A.G. (1957): Solution of the equation of bending for some classes of surfaces. Usp. Mat. Nauk 12, No. 2, 147–150 (Russian), Zbl.85,366
Efimov, N.V. (1948a): Qualitative questions of the theory of deformations of surfaces. Usp. Mat. Nauk 3, No. 2, 47–158. Engl, transi.: Am. Math. Soc. Transi. 6, 274–323, Zbl.30,69
Efimov, N.V. (1948b): Qualitative questions of the theory of deformations of surfaces “in the small”. Tr. Mat. Inst. Steklova 30, 1–128 (Russian), Zbl.41,488
Efimov, N.V. (1948c): On rigidity in the small. Dokl. Akad. Nauk SSSR 60, 761–764 (Russian), Zbl.39,382
Efimov, N.V. (1952): Some theorems about rigidity and non-bendability. Usp. Mat. Nauk 7, No. 5, 215–224 (Russian), Zbl.47,150
Efimov, N.V. (1958): A survey of some results on qualitative questions of the theory of surfaces. Proc. 3th All-Union Congr. of Math. 1956, Acad. Sci. Moscow, Vol. 3, 401–407, Zbl.87,361
Efimov, N.V., Usmanov, Z.D. (1973): Infinitesimal bendings of surfaces with a flat point. Dokl. Akad. Nauk SSSR 208, 28–31. Engl, transi.: Sov. Math. Dokl. 14, 22–25 (1973), Zbl.289.53005
Fogelsanger, A. (1987): The generic rigidity of minimal cycles. Preprint, Cornell Univ. 60 pp.
Fomenko, V.T. (1962): Investigation of solutions of the basic equations of the theory of surfaces. Dokl. Akad. Nauk SSSR 144, 69–71. Engl, transi.: Sov. Math. Dokl. 3,686–689 (1962), Zbl.l 17,383
Fomenko, V.T. (1965): Bending of surfaces with preservation of congruence points, Mat. Sb., Nov. Ser. 66, 127–141 (Russian), Zbl.192,272
Gluck, H. (1975): Almost all simple connected closed surfaces are rigid. Lect. Notes Math. 438, 225–239, Zbl.315.50002
Gluck, H., Krigelman, K., Singer, D. (1974): The converse to the Gauss-Bonnet theorem in PL. J. Differ. Geom. 9, 601–616, Zbl.294,57014
Goldstein, R.A., Ryan, P.J. (1975): Infinitesimal rigidity of submanifolds. J. Differ. Geom. 10, 49–60, Zbl.302.53029
Griffiths, P.A., Jensen, G.R. (1987): Differential systems and isometric embeddings. Ann. of Math. Stud., No. 114, Zbl.637.53001
Gromov, M.L., Rokhlin, V.A. (1970): Immersions and embeddings of Riemannian manifolds. Usp. Mat. Nauk 25, No. 5, 3–62. Engl, transi.: Russ. Math. Surv. 25, No. 5,1–57 (1970), Zbl.202,210
Gulliver, R.D., Osserman, R., Royden, H.L. (1973): A theory of branched immersions of surfaces. Am. J. Math. 95, 750–812, Zbl.295.53002
Hartman, P., Wintner, A. (1951): Gaussian curvature and local embedding. Am. J. Math. 73, 876–884, Zbl.44,184
Hartman, P., Wintner, A. (1952): On hyperbolic partial differential equations. Am. J. Math. 74, 834–876, Zbl.48,333
Hellwig, G. (1955): Über die Verbiegbarkeit von Flächenstucken mit positiver Gausscher Krümmung. Arch. Math. 6, 243–249, Zbl.64,158
Höesli, R. (1950): Spezielle Flächen mit Flächpunkten und ihre lokale Verbiegbarkeit. Compos. Math. 8, 113–141, Zbl.38,335
Hong, J., Zuily, C. (1987): Existence of C∞ local solutions for the Monge-Ampère equation. Invent. Math. 89, 645–661, Zbl.648.35016
Hopf, H., Schilt, H. (1938): Über Isometrie und stetige Verbiegung von Flächen. Math. Ann. 116, 58–75, Zbl.19,20
Isanov, T.G. (1977): On the extension of infinitesimal bendings. Dokl. Akad. Nauk SSSR 234, 1257–1260. Engl, transi.: Sov. Math. Dokl. 18, 842–846 (1977), Zbl.376.53002
Ivanova-Karatopraklieva, I. (1982–1983): Properties of the fundamental field infinitesimal bendings of a surface of revolution. God. Sofij. Univ. Fak. Mat. Mekh. 76, 21–40 (Bulgarian), Zbl.637.53005
Ivanova-Karatopraklieva, I. (1987–1988): Infinitesimal third-order bendings of surfaces of revolution with flattening at the pole. Ann. Univ. Sofia Fac. Math. Mec. 81 (to appear), (Russian)
Ivanova-Karatopraklieva, I. (1988): Infinitesimal bendings of surfaces of mixed curvature. Proc. XVII Spring Conf. of the Union of Bulgarian Math. pp. 49–56
Ivanova-Karatopraklieva, I. (1990): Infinitesimal bendings of higher order of rotational surfaces. Compt. Rend, de l’Acad. Bulgare des Sci. 43, No. 12
Ivanova-Karatopraklieva, I., Sabitov, I.Kh. (1989): Infinitesimal second-order bendings of surfaces of revolution with flattening at the pole. Mat. Zametki 45, 28–35. Engl, transi.: Math. Notes 45, No. 112,19–24 (1989), Zbl.662.53003
Ivanova-Karatopraklieva, I., Sabitov, I.Kh. (1991): Bendings of surfaces. I. Problems of Geometry 23, 131–184 (Russian)
Ivanova-Karatopraklieva, I., Sabitov, I.Kh. (1992): Bendings of surfaces. II. Problems of Geometry 24 (to appear) (Russian)
Jacobowitz, H. (1972a): Extending isometric embeddings. J. Differ. Geom. 9, 291–307, Zbl.283.53025
Jacobowitz, H. (1972b): Implicit function theorems and isometric embeddings. Ann. Math., II. Ser. 95, 191–225, Zbl.214,129
Jacobowitz, H. (1982a): Local analytic isometric deformations. Indiana Univ. Math. J. 31, No. 1, 47–55, Zbl.502.53004
Jacobowitz, H. (1982b): Local isometric embeddings. Semin. Differ. Geom., Ann. Math. Stud. 102, 381–393, Zbl.481.53018
Kann, E. (1970): A new method for infinitesimal rigidity of surfaces with K ≥ 0. J. Differ. Geom. 4, 5–12, Zbl. 194,525
Klimentov, S.B. (1982): On the structure of the set of solutions of the basic equations of the theory of surfaces. Ukr. Geom Sb. 25, 69–82 (Russian), Zbl.509.53021
Klimentov, S.B. (1984): On the extension of higher-order infinitesimal bendings of a simply-connected surface of positive curvature. Mat. Zametki 36, 393–403. Engl, transi.: Math. Notes 36, 695–700 (1984), Zbl.581.53002
Kuiper, N. (1955): On C1-isometric imbeddings. I, II. Nederl. Akad. Wetensch. Proc. Ser. A 58 (Indagationes Math. 17) 545–556; 683–689, Zbl.67,396
Kuiper, N. (1979): Sphères polyédriques flexibles dans E 3, d’après Robert Connelly. Lect. Notes Math. 710, 147–168, Zbl.435.53043
Kuznetsov, V.A. (1987): The structure of a neighbourhood of an isolated zero of the Lipschitz-Killing curvature on an m-dimensional surface in E n . Proc. All-Union Conf. on Geometry “in the large”. Inst. Math. Sib. Division of the USSR Academy of Sciences, Novosibirsk, p. 64
Lashchenko, D.V. (1987): On the rigidity “in the small” of certain classes of hyper surfaces. (Deposited at VINITI, No. 3258, pp. 1–21)
Lashchenko, D.V. (1989): On the rigidity “in the small” of certain classes of surfaces. (Deposited at VINITI, No. 2121, pp. 1–23)
Lebesgue, H. (1902): Intégrale, longueur, aire. Ann. Math. Pura Appl. (3) 7, 231–359, Jbuch 33, 307
Lebesgue, H. (1967): Octaèdres articulés de Bricard. Enseign. Math., IL Ser. 13, 175–185, Zbl.155,493
Legendre, A. (1806): Eléments de géométrie. 6th ed.,
Paris Lin, CS. (1985): The local isometric embedding in R 3 of two-dimensional Riemannian manifolds with non-negative curvature. J. Differ. Geom. 27, 213–230, Zbl.584.53002
Lin, C.S. (1986): The local isometric embedding in R 3 of two-dimensional Riemannian manifolds with Gaussian curvature changing sign cleanly. Commun. Pure Appl. Math. 39, 867–887, Zbl.612.53013
Makarova, Z.T. (1953): Investigation of an integral invariant of binary forms of degree n > 4. Mat. Sb., Nov. Ser. 33, 233–240 (Russian), Zbl.52,17
Maksimov, I.G. (1987): Investigation of the bendability of polyhedra with few vertices. Proc. All-Union Conf. on Geometry “in the large”. Inst. Math. Siberian Division of the USSR Academy of Sciences, Novosibirsk, p. 75 (Russian)
Markov, P.E. (1980): Infinitesimal bendings of some multidimensional surfaces, Mat. Zametki 27, 469–479. Engl, transi.: Math. Notes 27, 232–237 (1980), Zbl.436.53052
Markov, P.E. (1987): Infinitesimal higher-order bendings of multidimensional surfaces in spaces of constant curvature, Mat. Sb., Nov. Ser. 133, 64–85. Engl, transi.: Math. USSR, Sb. 61, No. 1,65–85 (1988), Zbl.629.53020
Milka, A.D. (1973): Continuous bendings of convex surfaces, Ukr. Geom. Sb. 13, 129–141 (Russian) Zbl.288.53045
Milka, A.D. (1986): What is geometry “in the large”?, Nov. Zh. Nauk. Tekhn. Ser. “Mat. Kibernet.” 3, 3–31 (Russian)
Nakamura, G., Maeda, Y. (1985): Local isometric embedding of 2-dimensional Riemannian manifolds into R 3 with nonpositive Gaussian curvature, Proc. Japan Acad., Ser. A 61, 211–212
Nash, J. (1954): CMsometric embeddings, Ann. Math., II. Ser. 60, 383–396, Zbl.58,377
Nirenberg, L. (1963): Rigidity of a class of closed surfaces, in: Nonlinear problems, Proc. Symp. Madison 1962, 177–193, Zbl. 111,344
Pogorelov, A.V. (1967): Geometrical methods in the nonlinear theory of elastic shells, Nauka, Moscow (Russian) Zbl. 168,456
Pogorelov, A.V. (1969): Extrinsic geometry of convex surfaces, Nauka, Moscow. Engl, transi.: Am. Math. Soc, Providence, RI, 1973, Zbl.311.53067
Pogorelov, A.V. (1986): Bendings of Surfaces and Stability of the Shells. Nauka, Moscow: Engl. transi.: Providence, RI (1988), Zbl.616.73051
Poznyak, E.G. (1959): A relation between non-rigidity of the first and second order for surfaces of revolution, Usp. Mat. Nauk 14, No. 6, 179–184 (Russian), Zbl.97,370
Poznyak, E.G. (1960): Nonrigid closed polyhedra, Vestn. Mosk. Univ. Ser. I. 15, No. 3, 14–19 (Russian), Zbl.98,354
Poznyak, E.G. (1973): Isometric immersions of two-dimensional Riemannian metrics in Euclidean spaces, Usp. Mat. Nauk 28, No. 4, 47–76. Engl, transi.: Russ. Math. Surv. 28, No. 4, 47–77 (1973), Zbl.283.53001
Poznyak, E.G., Sokolov, D.D. (1977): Isometric immersions of Riemannian spaces in Euclidean spaces. Itogi Nauki Tekh., Ser. Algebra, Topologija, Geom. 15,173–211. Engl, transi.: J. Sov. Math. 14, 1407–1428 (1980), Zbl.448.53040
Reshetnyak, Yu.G. (1962): Nonrigid surfaces of revolution. Sib. Mat. Zh. 3, 591–604 (Russian), Zbl. 119,372
Reshetnyak, Yu.G. (1982): Stability theorems in geometry and analysis. Nauka, Novosibirsk (Russian), Zbl.523.53025
Sabitov, I.Kh. (1965a): The local structure of Darboux surfaces. Dokl. Akad. Nauk SSSR 162, 1001–1004. Engl, transi.: Sov. Math. Dokl. 6, 804–807 (1965), Zbl.131,193
Sabitov, I.Kh. (1965b): Some results on infinitesimal bendings of surfaces “in the small” and “in the large”. Dokl. Akad. Nauk SSSR 162, 1256–1258. Engl, transi.: Sov. Math. Dokl. 6,862–864 (1965), Zbl.131,193
Sabitov, I.Kh. (1967): A minimal surface as the rotation graph of a sphere. Mat. Zametki 2, 645–656. Engl, transi.: Math. Notes 2, 881–887 (1968), Zbl.162,247
Sabitov, I.Kh. (1973): Rigidity of “corrugated” surfaces of revolution. Mat. Zametki 14, 517–522. Engl, transi.: Math. Notes 14, 854–857 (1973), Zbl.283.53004
Sabitov, LKh. (1979a): Infinitesimal bendings of surfaces of revolution with exponential flattening at the pole. Proc. 7th All-Union Conf. on modern problems of geometry. Beloruss. State Univ., Minsk, p. 240
Sabitov, I.Kh. (1979b): Trough, Mat. Entsiklopediya. Vol. 2, p. 409. Engl, transi, in: Encycl. Math., Reidel, Dordrecht, 1988
Sabitov, I.Kh. (1983): Description of bendings of degenerate suspensions. Mat. Zametki 33, 901–914. Engl, transi.: Math. Notes 33,462–468 (1983), Zbl.528.51012
Sabitov, I.Kh. (1986): Investigation of the rigidity and non-bendability of analytic surfaces of revolution with flattening at the pole. Vestn. Mosk. Univ., Ser. 11986, No. 5, 29–36. Engl, transi.: Mose. Univ. Math. Bull. 41, No. 5, 33–41 (1986), Zbl.633.53006
Sabitov, I.Kh. (1987): Some results and problems of the local theory of bendings. Proc. All-Union Conf. on geometry in the large, Inst. Math. Siberian Division of the USSR Academy of Sciences, Novosibirsk, p. 108 (Russian)
Sabitov, I.Kh. (1988): Isometric immersions and embeddings of locally Euclidean metrics in R 2 . Tr. Semin. Vektorn. Tenzorn. Anal. 23, 147–156 (Russian)
Sabitov, I.Kh. (1989): New classes of unbendable polyhedra. Proc. All-Union Conf. on geometry and analysis, Inst. Math. Siberian Division of the USSR Academy of Sciences, Novosibirsk, p. 72 (Russian)
Sauer, R. (1935): Infinitesimale Verbiegungen zueinander projektiver Flächen. Math. Ann. 111, 71–82, Zbl.10,374
Sauer, R. (1948): Projektive Transformationen des Darboux’schen Flächenkranzes. Arch. Math. 1, 89–93, Zbl.31,269
Schilt, H. (1937): Über die isolierten Nullstellen der Flächenkrümmung und einige Verbiegkeitssätze. Compos. Math. 5, 239–283, Zbl.18,169
Sen’kin, E.P. (1978): Bending of convex surfaces. Itogi Nauki Tekh., Ser. Probl. Geom. 10, 193–222 (Russian). Engl, transi.: J. Sov. Math. 14,1287–1305 (1980), Zbl.423.53047
Shor, L.A. (1962): An example of a discontinuum of nontrivially isometric convex surfaces. Usp. Mat. Nauk 17, No. 5, 157–160 (Russian), Zbl.168,424
Sinyukov, N.S. (1986): On the development of modern differential geometry in Odessa State University in recent years. Izv. Vyssh. Uchebn. Zaved., Mat., No. 1, 69–74. Engl, transi.: Soviet Math. 30, No. 1, 92–99 (1986), Zbl.602.01031
Spivak, M. (1979): A comprehensive introduction to differential geometry. Vol. 5, 2nd. ed., Publish or Perish, Berkeley, CA, Zbl.306.53003
Tartakovskij, V.A. (1953): The JV-invariant of N.V. Efimov in the theory of bending of surfaces. Mat. Sb., Nov. Ser. 32, 225–248 (Russian), Zbl.50,160
Trotsenko, D.A. (1980): Non-rigid analytic surfaces of revolution. Sib. Mat. Zh. 21, No. 5, 100–108. Engl, transi.: Sib. Math. J. 21, 718–724 (1980), Zbl.467.53001
Usmanov, Z.D. (1984): Infinitesimal bendings of surfaces of positive curvature with a flat point, in: Differential Geometry, Warsaw 1979, Banach Cent. Publ. 12, 241–272 (Russian), Zbl.559.53002
Vasifeva, A.B., Butuzov, V.F. (1978): Singularly perturbed equations in critical cases. Moscow Univ. Press. Moscow (Russian)
Vekua, I.N. (1959): Generalized analytic functions. Fizmatgiz, Moscow. Engl, transi.: Pergamon Press, London-Paris-Frankfurt; Addison-Wesley, Reading, MA, 1962, Zbl.92,297
Vekua, I.N. (1982): Some general methods of constructing different versions of the theory of shells. Nauka, Moscow, Zbl.598.73100. Engl, transi.: Pitman, Boston etc., 1985
Vincensini, P. (1962): Sur les propriétés géométriques des transformations infinitésimales des surfaces et ses relations avec la théorie de congruences des sphères. Ann. Sci. Éc. Norm. Super., HI. Ser. 79, 299–319, Zbl.108,345
Vojtsekhovskij, M.I. (1977): Infinitesimal bending. Mat. Entsiklopediya, Vol. 1, p. 435. Engl, transi. in: Encycl. Math., Reidel, Dordrecht, 1988
Vojtsekhovskij, M.I. (1979): Darboux surfaces. Mat. Entsiklopediya Vol. 2, p. 16. Engl, transi, in: Encycl. Math., Reidel, Dordrecht, 1988
Whiteley, W. (1984): Infinitesimally rigid polyhedra. I. Statics of frameworks. Trans. Am. Math. Soc. 285, 431–465, Zbl.518.52010
Whiteley, W. (1987a): Applications of the geometry of rigid structures. Proc. Conf. on computer-aided geometric reasoning (Sophia-Antipolis, 1987), Vol. II,.INRIA, Rocquencourt, pp. 217–251
Whiteley, W. (1987b): Rigidity and polarity. I. Statics of sheet structures. Geom. Dedicata 22, 329–362, Zbl.618.51006
Yanenko, N.N. (1952): Some necessary conditions for bendable surfaces V m in (m + q)-dimensional Eudlidean space. Tr. Semin. Vektorn. Tenzorn. Anal. 9, 236–287 (Russian), Zbl.48,389
Yanenko, N.N. (1954): On the theory of embedding of surfaces into multidimensional Eudlidean space. Trudy Mosk. Mat. O.-va 3, 89–180 (Russian), Zbl.58,156
Zalgaller, V.A. (1962): Possible singularities of smooth surfaces. Vestn. Leningr. Univ. 17, No. 7 (Ser. Mat. Mekh. Astron. No. 2), 71–77 (Russian), Zbl.122,170
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Sabitov, I.K. (1992). Local Theory of Bendings of Surfaces. In: Burago, Y.D., Zalgaller, V.A. (eds) Geometry III. Encyclopaedia of Mathematical Sciences, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02751-6_3
Download citation
DOI: https://doi.org/10.1007/978-3-662-02751-6_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08102-6
Online ISBN: 978-3-662-02751-6
eBook Packages: Springer Book Archive