Timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space

Details Timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space Timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space

2006-07-04

arxiv.org/abs/math/0607104v2

Mathematics

Differential Geometry

47 pages, 24 figures, references revised, Annals of Global Analysis and Geometry

Scientific paper

10.1007/s10455-006-9030-z

It is shown that timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space can be constructed from a pair of Lorentz holomorphic and Lorentz antiholomorphic null curves in PSL(2,R) via Bryant type representation formulae. These formulae are used to investigate an explicit one-to-one correspondence, the so-called Lawson correspondence, between timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space and timelike minimal surfaces in Minkowski 3-space. The hyperbolic Gauss map of timelike surfaces in anti-de Sitter 3-space, 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 anti-de Sitter 3-space. In particular, the relationship between the Lorentz holomorphicity of the hyperbolic Gauss map and timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space is studied.

Affiliated with

Also associated with

No associations

Rating

Timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Timelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-450673