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

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dc.creatorLee, Sungwook
dc.date2006-07-04
dc.date2006-07-10
dc.date.accessioned2026-07-07T07:18:01Z
dc.date.available2026-07-07T07:18:01Z
dc.descriptionIt 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.
dc.description47 pages, 24 figures, references revised, Annals of Global Analysis and Geometry
dc.identifierhttps://arxiv.org/abs/math/0607104
dc.identifierhttp://arxiv.org/abs/math/0607104
dc.identifierdoi:10.1007/s10455-006-9030-z
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114153
dc.subjectDifferential Geometry
dc.subject53A10; 53C42; 53C50
dc.titleTimelike surfaces of constant mean curvature 1 in anti-de Sitter 3-space
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