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Isoparametric Surfaces in 3－dimensional De Sitter Space and Anti－de Sitter Space

李梅, 赵永波

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Abstract

A spacelike surface M in 3-dimensional de sitter space S1^3 or 3-dimensional anti-de Sitter space H1^3 is called isoparametric, if M has constant principal 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 surfaces in S1^3 and H1^3.

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A spacelike surface M in 3-dimensional de sitter space S1^3 or 3-dimensional anti-de Sitter space H1^3 is called isoparametric, if M has constant principal 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 surfaces in S1^3 and H1^3.

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Available abstract

A spacelike surface M in 3-dimensional de sitter space S1^3 or 3-dimensional anti-de Sitter space H1^3 is called isoparametric, if M has constant principal 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 surfaces in S1^3 and H1^3.

Key concepts: De Sitter space, Anti-de Sitter space, Constant (computer programming), De Sitter universe, Space (punctuation), Surface (topology), de Sitter invariant special relativity, Mathematics

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