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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Isothermic surfaces and the Gauss map


Author: Bennett Palmer
Journal: Proc. Amer. Math. Soc. 104 (1988), 876-884
MSC: Primary 53C42
DOI: https://doi.org/10.1090/S0002-9939-1988-0964868-7
MathSciNet review: 964868
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Abstract: We give a necessary and sufficient condition for the Gauss map of an immersed surface $ M$ in $ n$-space to arise simultaneously as the Gauss map of an anti-conformal immersion of $ M$ into the same space. The condition requires that the lines of curvature of each normal section lie on the zero set of a harmonic function. The result is applied to a class of surfaces studied by S. S. Chern which admit an isometric deformation preserving the principal curvatures.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0964868-7
Article copyright: © Copyright 1988 American Mathematical Society