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The Gauss map of minimal surfaces in the Anti-de Sitter space

Jorge H.S. de Lira - No affiliation found

2011/03/01 Full-length article DOI: 10.1016/j.geomphys.2010.11.009 Journal: Journal of Geometry and Physics

Abstract:

AbstractIt is proved that a pair of spinors satisfying a Dirac-type equation represent surfaces immersed in Anti-de Sitter space with prescribed mean curvature. Here, we consider Anti-de Sitter space as the Lie group SU1,1 endowed with a one-parameter family of left-invariant metrics where only one of them is bi-invariant and corresponds to the isometric embedding of Anti-de Sitter space as a quadric in R2,2. We prove that the Gauss map of a minimal surface immersed in SU1,1 is harmonic. Conversely, we exhibit a representation of minimal surfaces in Anti-de Sitter space in terms of a given harmonic map.