Mathematics and Natural Sciences
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.
Annals of Global Analysis and Geometry
(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