Bonnet pairs and isothermic surfaces

Duke Mathematical Journal

Volumn 92, Issue 3, 1998, Pages 637-644

  Kamberov, George ^a   Pedit, Franz ^a   Pinkall, Ulrich ^b  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009265338     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-98-09219-5     Document Type: Article

References (10)

1. A. Bobenko and U. Eitner, Bonnet surfaces and Painlevé equations, Sonderforschungsbereich 288, Technische Universität Berlin, preprint 151, 1994.
2. A. Bobenko and U. Pinkall, Discrete isothermic surfaces, J. Reine Angew. Math. 475 (1996), 187-208.
3. O. Bonnet, Memoire sur la theorie des surfaces applicables, J. École Polytechnique 42 (1867), 72-92.
4. F. Burstall, U. Hertrich-Jeromin, F. Pedit, and U. Pinkall, Curved flats and isothermic surfaces, Math. Z. 225 (1997), 199-209.
5. E. Cartan, Sur les couples de surfaces applicables avec conservation des courbures principales, Bull. Sei. Math. (2) 66 (1942), 55-72.
6. S.-S. Chern, “Deformations of surfaces preserving principal curvatures” in Differential Geometry and Complex Analysis: A volume dedicated to the memory of H. E. Rauch, Springer-Verlag, Berlin, 1985, 155-163.
7. U. Hertrich-Jeromin and F. Pedit, Remarks on the Darboux transform of isothermic surfaces, Doc. Math. DMV 2 (1997), 313-333.
8. G. Kamberov, “Recovering the shape of a surface from the mean curvature” in Proceedings of the International Conference on Dynamical Systems and Differential Equations, ed. W. Chen and S. C. Hu, Dekker, to appear.
9. H. B. Lawson Jr. and R. Tribuzy, On the mean curvature function for compact surfaces, J. Differential Geom. 16 (1981), 179-183.
10. U. Pinkall, Regular homotopy classes of immersed surfaces, Topology 24 (1985), 421-434.