Isothermic surfaces and the Gauss map

Palmer, Bennett

doi:10.1090/S0002-9939-1988-0964868-7

Isothermic surfaces and the Gauss map
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Proc. Amer. Math. Soc. 104 (1988), 876-884 Request permission

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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