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Preprint 657-1999

Isoparametric surfaces in 3-dimensional de Sitter space and anti-de Sitter space

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Author(s) : Huili Liu, Guosong Zhao

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 657-1999

MSC 2000

53C50 Lorentz manifolds, manifolds with indefinite metrics
53C40 Global submanifolds

Abstract :
A spacelike surface $M$ in 3-dimensional de Sitter space $\mathbb{S}^3_1$ or 3-dimensional anti-de Sitter space $\mathbb{H}^3_1$ is called isoparametric, if $M$ has constant principle curvatures. A timelike surface is called isoparametric, if its minimal polynomial of the shape operator is constant. In this paper, we determine the spacelike isoparametric surfaces and the timelike isoparametric surfacesx in $\mathbb{S}^3_1$ and $\mathbb{H}^3_1$.

Keywords : isoparametric surface, de Sitter and anti-de Sitter space, principal curvature

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