CLASSES OF HYPERSURFACES WITH VANISHING LAPLACE INVARIANTS

Title & Authors
CLASSES OF HYPERSURFACES WITH VANISHING LAPLACE INVARIANTS
Riveros, Carlos M.C.; Corro, Armando M.V.;

Abstract
Consider a hypersurface $\small{M^n}$ in $\small{\mathbb{R}^{n+1}}$ with $\small{n}$ distinct principal curvatures, parametrized by lines of curvature with vanishing Laplace invariants. (1) If the lines of curvature are planar, then there are no such hypersurfaces for $\small{n{\geq}4}$, and for $\small{n=3}$, they are, up to M$\small{\ddot{o}}$bius transformations Dupin hypersurfaces with constant M$\small{\ddot{o}}$bius curvature. (2) If the principal curvatures are given by a sum of functions of separated variables, there are no such hypersurfaces for $\small{n{\geq}4}$, and for $\small{n=3}$, they are, up to M$\small{\ddot{o}}$bius transformations, Dupin hypersurfaces with constant M$\small{\ddot{o}}$bius curvature.
Keywords
lines of curvature;Laplace invariants;Dupin hypersurfaces;
Language
English
Cited by
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