#### Title

Timelike Surfaces of Constant Mean Curvature +/- 1 In Anti-de Sitter 3-space H-1(3)(-1)

#### Document Type

Article

#### Publication Date

6-1-2006

#### Department

Mathematics

#### Abstract

It is shown that timelike surfaces of constant mean curvature +/- 1 in anti-de Sitter 3-space H-1(3)(- 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-1(3). The hyperbolic Gauss map of timelike surfaces in H-1(3)(- 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 H-1(3)(- 1). In particular, the relationship between the Lorentz holomorphicity of the hyperbolic Gauss map and timelike surface of constant mean curvature +/- 1 in H-1(3)(- 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 H-1(3)(-1). *Annals of Global Analysis and Geometry, 29*(4), 361-407.

Available at: http://aquila.usm.edu/fac_pubs/2357