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Taimanov's surface evolution and Bäcklund transformations for curves
Author(s):
Oscar
Garay;
Joel
Langer
Journal:
Conform. Geom. Dyn.
3
(1999),
37-49.
MSC (1991):
Primary 35Q51, 35Q53, 53A05, 53A35, 53A30
Posted:
March 25, 1999
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Abstract:
Taimanov's evolution of conformally parametrized surfaces in Euclidean space by the modified Novikov-Veselov equation is interpreted here (in the revolution case) using hyperbolic geometry and Bäcklund transformations for curves.
References:
- [C-I]
- A. Calini and T. Ivey, Bäcklund transformations and knots of constant torsion, J. Knot Theory and its Ramifications 7 (1998), p. 719. CMP 99:01
- [Ch]
- B. Y. Chen, Some conformal invariants of submanifolds and their applications, Bol. Un. Mat. Ital. (4) 10 (1974). MR 51:6663
- [G-P]
- R. Goldstein and D. Petrich, The Korteweg-de Vries hierarchy as dynamics of closed curves in the plane, Phys. Rev. Lett. 67 (1991), p. 3203. MR 92g:58050
- [Iv]
- T. Ivey, Helices, Hasimoto surfaces and Bäcklund transformations, Preprint (1998).
- [Ko]
- B. Konopelchenko, Induced surfaces and their integrable dynamics, Studies in Appl. Math. 96 (1996), p. 9. MR 96i:53011
- [La]
- G. Lamb, Solitons and the motion of helical curves, 37 (1976), p. 235. MR 57:13250
- [L-P 1]
- J. Langer and R. Perline, Poisson geometry of the filament equation, J. Nonlinear Sci. 1 (1991), p. 71. MR 92k:58118
- [L-P 2]
- J. Langer and R. Perline, Local geometric invariants of integrable evolution equations, J. Math. Phys. 35 (1994), p. 1732. MR 95c:58095
- [L-P 3]
- J. Langer and R. Perline, Curve motion inducing modified Korteweg-de Vries systems, Phys. Lett. A 239 (1998), pp. 37-49. CMP 98:10
- [L-S 1]
- J. Langer and D. Singer, The total squared curvature of closed curves, J. Diff. Geom. 20 (1984), pp. 37-49. MR 86i:58030
- [L-S 2]
- J. Langer and D. Singer, Curves in the hyperbolic plane and mean curvature of tori in 3-space, Bull. London Math Soc. 16 (1984), pp. 37-49. MR 85k:53006
- [Ro]
- C. Rogers, Bäcklund transformations in soliton theory, in Soliton theory: a survey of results, ed. A. P. Fordy, St. Martin's Press, 1990. CMP 91:07
- [Ta 1]
- I. Taimanov, Modified Novikov-Veselov equation and differential geometry of surfaces, Preprint November 1995 (da-ga 9511005), Translations Amer. Math. Soc., Ser. 2, 179, 1997. MR 98c:53071
- [Ta 2]
- I. Taimanov, Surfaces of revolution in terms of solitons, Ann. Global Analysis and Geom. 15 (1997), pp. 37-49. CMP 98:04
- [We]
- J. Weiner, On a problem of Chen, Willmore, et al., Indiana Univ. Math. J. 27 (1978), pp. 37-49. MR 57:7466
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Additional Information:
Oscar
Garay
Affiliation:
Department of Mathematics, Universidad Pais Vasco, Bilbao, Spain
Email:
mtpgabeo@lg.ehu.es
Joel
Langer
Affiliation:
Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
Email:
jxl6@po.cwru.edu
DOI:
10.1090/S1088-4173-99-00043-0
PII:
S 1088-4173(99)00043-0
Received by editor(s):
October 28, 1998
Posted:
March 25, 1999
Additional Notes:
We wish to acknowledge the support of the Departamento De Educacion, Universidades E Investigacion, Gobierno Vasco, for J. Langer's visit.
Copyright of article:
Copyright
1999,
American Mathematical Society
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