Classes of hypersurfaces with vanishing Laplace invariants
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2012
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Consider a hypersurface M n in R n+1 with n distinct princi-
pal curvatures, parametrized by lines of curvature with vanishing Laplace
invariants.
(1) If the lines of curvature are planar, then there are no such hyper-
surfaces for n ≥ 4, and for n = 3, they are, up to Möbius transformations,
Dupin hypersurfaces with constant Möbius curvature.
(2) If the principal curvatures are given by a sum of functions of sepa-
rated variables, there are no such hypersurfaces for n ≥ 4, and for n = 3,
they are, up to Möbius transformations, Dupin hypersurfaces with con-
stant Möbius curvature.
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RIVEROS, Carlos M. C.; CORRO, Armando M. V. Classes of hypersurfaces with vanishing Laplace invariants. Bulletin of the Korean Mathematical Society, Seoul, v. 49, p. 685-692, 2012.