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The Cauchy-Riemann equations and differential geometry
Author(s):
R. O.
Wells Jr.
Journal:
Bull. Amer. Math. Soc.
6
(1982),
187-199.
MSC (1980):
Primary 32-02, 53-01
MathSciNet review:
640945
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References:
- 1.
- M. F. Atiyah, Geometry of Yang-Mills fields, Lezioni Fermione, Acad. Naz. dei Lincei, Scuola Normale Sup., Pisa, 1979. MR 554924
- 2.
- M. S. Baouendi and F. Treves, A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. of Math. (2) 113 (1981), 387-421. MR 607899
- 3.
- S. Bergman, The kernel function and conformal mapping, Math. Surveys, no. 5, Amer. Math. Soc., Providence, R.I., 1950. MR 38439
- 4.
- H. Behnke and P. Thullen, Theorie der Funktionen mehrerer komplexer Veränderlichen, 2nd ed., Ergebnisse der Math, und ihrer Grenzgebiete Band 51, Springer-Verlag, Berlin-New York, 1970. MR 271391
- 5.
- S. Bochner, Analytic and meromorphic continuation by means of Green's formula, Ann. of Math. (2) 44 (1943), 652-673. MR 9206
- 6.
- L. Boutet de Monvel, Integration des equations de Cauchy-Riemann induites formelles, Sèminaire Goulaouic-Lions-Schwartz (1974-75), Exposé No. 9, Centre Math. École Polytech., Paris, 1975. MR 409893
- 7.
- A. Brown, On certain analytic continuations and analytic homeomorphisms, Duke Math. J. 2 (1936), 20-28. MR 1545903
- 8.
- R. Bryant, Space-times and CR-manifolds, Trans. Amer. Math. Soc. (to appear). MR 656486
- 9.
- D. Burns and S. Shnider, Real hypersurfaces in complex manifolds, Proc. Sympos. Pure Math., vol. 30, Amer. Math. Soc., Providence, R. I., 1977, pp. 141-168. MR 450603
- 10.
- D. Burns, S. Shnider and R. O. Wells, Jr., Deformations of strongly pseudoconvex domains, Invent. Math. 46 (1978), 237-253. MR 481119
- 11.
- C. Carathéodory, Über das Schwarze Lemma bei analytischen Funktionen von zwei komplexen Veränderlichen, Math. Ann. 97 (1926), 76-98.
- 12.
- E. Cartan, Sur la géométrie pseudo-conforme des hypersurfaces de deux variables complexes. I, Ann. Math. Pura Appl. (4) 11 (1932), 17-90 (or Oeuvres. II, 2, 1231-1304); II, Ann. Scuola Norm. Sup. Pisa, (2) 1 (1932), 333-354 (or Oeuvres. III, 2, 1217-1238). MR 1556687
- 13.
- S. S. Chern, On the projective structure of a real hypersurface in Cn+1, Math. Scand. 36 (1975), 74-82. MR 379910
- 14.
- S. S. Chern and J. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271. MR 425155
- 15.
- P. Dippolito, Universal bundles for deformations of asymetric structures, Trans. Amer. Math. Soc. (to appear). MR 648080
- 16.
- James Faran, Segre families and hypersurfaces, Invent. Math. 60 (1980), 135-172. MR 586425
- 17.
- C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65. MR 350069
- 18.
- C. Fefferman, Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains, Ann. of Math. (2) 103 (1976), 395-416. MR 407320
- 19.
- C. Fefferman, Parabolic invariant theory in complex analysis, Advances in Math. 31 (1979), 131-262. MR 526424
- 20.
- G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Ann. of Math. Studies, no. 75, Princeton Univ. Press, Princeton, N. J., 1972. MR 461588
- 21.
- H. Granert and R. Remmert, Analytische Stellenalgebren, Springer, Berlin-Heidelberg-New York, 1971. MR 316742
- 22.
- R. Greene and S. Krantz, Deformation of complex structures, estimates for the {$\bar\partial $} equation, and stability of the Bergman kernel, Adv. in Math. (to appear). MR 644667
- 23.
- R. C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Englewood Cliffs, N. J., 1965. MR 180696
- 24.
- F. Hartogs, Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen insbesondere über die Darstellung derselben durch Reihen, welche nach Potenzen einer Veränderlichen fortschreiten, Math. Ann. 62 (1906), 1-80. MR 1511365
- 25.
- L. Hörmander, Linear partial differential operators, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 161012
- 26.
- L. Hörmander, An introduction to complex analysis in several variables, North-Holland, Amsterdam, 1973. MR 1045639
- 27.
- David S. Johnson, Biholomorphic equivalence in a class of graph domains, Indiana J. Math. 29 (1980), 341-348. MR 570685
- 28.
- A. Krzoska, Über die naturlichen Grenzen der analytischen Funktionen mehrerer Veränderlicher, Dissertation, Greifswald, 1933.
- 28a. C. R. LeBrun, Jr., Spaces of complex geodesics and related structures, Thesis, Oxford University, 1980.
- 29.
- E. E. Levi, Studii sui punti singolari essenziale delle funzioni analitiche di due o più variabili complesse, Annali di Mat. 17 (1909), 61-87.
- 30.
- H. Lewy, On the local character of the solutions of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, Ann. of Math. (2) 64 (1956), 514-522. MR 81952
- 31.
- H. Lewy, On hulls of holomorphy, Comm. Pure. Appl. Math. 13 (1960), 587-591. MR 150339
- 32.
- J. Moser, Holomorphic equivalence and normal forms of hypersurfaces, Proc. Sympos. Pure Math., vol. 27, Part 2, Amer. Math. Soc., Providence, R. I., 1975, pp. 109-112. MR 435439
- 33.
- L. Nirenberg, Lectures on linear partial differential equations, CBMS Reg. Conf. Ser. in Math., no. 17, Amer. Math. Soc. Providence, R. I., 1973. MR 450755
- 34.
- R. Penrose, Nonlinear gravitons and curved twistor theory, Gen. Relativity and Gravitation 7 (1976), 31-52. MR 439004
- 35.
- H. Poincaré, Les functions analytique de deux variables et la représentation conforme, Rend. Circ. Math. Palermo 23 (1907), 185-220 (or Oeuvres. IV, 244-289).
- 36.
- W. F. Osgood, Lehrbuch der Funktionentheorie, 2nd. ed., vol. 2, part I, Teubner, Leipzig, 1929.
- 37.
- B. Segre, Questioni geometriche legate colla teoria delle funzioni di due variabili complesse, Rend. Sem. Mat. Roma 7 (1931), 59-107.
- 37.
- B. Segre, Interno al problema di Poincaré della rappresentazione pseudoconforme, Rend. Acc. Lincei 13 (1931), pp. 676-683.
- 38.
- F. Sommer, Komplex analytische Blätterung reeler Mannigfaltigkeiten im Cn, Math. Ann. 136 (1958), 111-133. MR 101924
- 39.
- N. Tanaka, On the pseudo-conformal geometry of hypersurfaces of the space of n complex variables, J. Math. Soc. Japan 14 (1962), 397-429. MR 145555
- 40.
- N. Tanaka, Graded Lie algebras and geometric structures, Proc. U.S.-Japan Seminar in Differential Geometry, (Kyoto, 1965), Nippon Hyoronsha, Tokyo, 1966, pp. 147-150. MR 222802
- 41.
- N. Tanaka, On non-degenerate real hypersurfaces, graded Lie algebras, and Cartan connections, Japan. J. Math. 2 (1976), 131-190. MR 589931
- 42.
- M. A. Tresse, Détermination des invariants ponctuels de l'equation différentielle ordinaire du second order y" = w (x, y, y'), S. Hirzel, Leipzig, 1896.
- 43.
- S. M. Webster, On the mapping problem for algebraic real hypersurfaces, Invent. Math. 43 (1977), 53-68. MR 463482
- 44.
- S. M. Webster, On the Moser normal form at a non-umbilic point, Math. Ann. 233 (1978), 97-102. MR 486511
- 45.
- S. M. Webster, The rigidity of CR-hypersurfaces in a sphere, Indiana Univ. Math. J. 28 (1979), 405-416. MR 529673
- 46.
- R. O. Wells, Jr., Function theory on differentiable submanfolds, Contributions to Analysis, Academic Press, New York, 1974, pp. 407-441. MR 357856
- 47.
- R. O. Wells, Jr., Complex manifolds and mathematical physics, Bull. Amer. Math. Soc. (N. S.) 1 (1979), 296-336. MR 520077
- 48.
- R. O. Wells, Jr., Complex geometry in mathematical physics, Univ. of Montreal Press (to appear). MR 654864
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Additional Information:
DOI:
10.1090/S0273-0979-1982-14976-X
PII:
S 0273-0979(1982)14976-X
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