Timelike Surfaces of Constant Mean Curvature ±1 In Anti-de Sitter 3-space H³₁)

Authors

Sungwook Lee, University of Southern MississippiFollow

Document Type

Article

Publication Date

6-1-2006

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

It is shown that timelike surfaces of constant mean curvature ± in anti-de Sitter 3-space H³ ₁(−1) can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL₂R via Bryant type representation formulae. These Bryant type representation formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson–Guichard correspondence, between timelike surfaces of constant mean curvature ± 1 and timelike minimal surfaces in Minkowski 3-space E ³ ₁. The hyperbolic Gauß map of timelike surfaces in H³ ₁(−1), which is a close analogue of the classical Gauß map is considered. It is discussed that the hyperbolic Gauß map plays an important role in the study of timelike surfaces of constant mean curvature ± 1 in H³ ₁(−1). In particular, the relationship between the Lorentz holomorphicity of the hyperbolic Gauß map and timelike surface of constant mean curvature ± 1 in H³ ₁(−1) is studied.

Publication Title

Annals of Global Analysis and Geometry

Volume

29

Issue

4

First Page

361

Last Page

407

Recommended Citation

Lee, S. (2006). Timelike Surfaces of Constant Mean Curvature ±1 In Anti-de Sitter 3-space H³₁). Annals of Global Analysis and Geometry, 29(4), 361-407.
Available at: https://aquila.usm.edu/fac_pubs/2357