Physical Sciences and Mathematics Commons^™

Timelike Surfaces Of Constant Mean Curvature ±1 In Anti-De Sitter 3-Space H31), Sungwook Lee

Faculty Publications

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 …