Title

Spacelike Surfaces of Constant Mean Curvature ±1 In de Sitter 3-space S31(1)

Document Type

Article

Publication Date

3-1-2005

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

It is shown that spacelike surfaces of constant mean curvature ±1 (abbreviated as CMC ±1) in de Sitter 3-space S31(1) can be constructed from holomorphic curves in PSL(2;C) = SL(2;C)/{±id} via a Bryant type representation formula. This Bryant type representation formula is used to investigate an explicit one-to-one correspondence, the so-called {Lawson correspondence}, between spacelike CMC ±1 surfaces in de Sitter 3-space S31(1) and spacelike maximal surfaces in Lorentz 3-space E31. The hyperbolic Gauss map of spacelike surfaces in S31(1), which is a close analogue of the classical Gauss map, is considered. It is shown that the hyperbolic Gauss map plays an important role in the study of spacelike CMC ± surfaces in S31(1). In particular, the relationship between the holomorphicity of the hyperbolic Gauss map and spacelike CMC ±1 surfaces in S31(1) is studied.

Publication Title

Illinois Journal of Mathematics

Volume

49

Issue

1

First Page

63

Last Page

98

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