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

Liu, Huili; Zhao, Guosong

Inst. Mathematik

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 $\mathbb{H}^3_1$.