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

作者：de Lira Jorge H S^*; Hinojosa Jorge A

来源：Journal of Geometry and Physics, 2011, 61(3): 610-623.

DOI：10.1016/j.geomphys.2010.11.009

• Minimal surfaces
• Harmonic maps
• Weierstrass representation
• Anti-de Sitter space

It 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 Antide Sitter space as the Lie group SU(1.1) 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 R(2.2). We prove that the Gauss map of a minimal surface immersed in SU(1.1) is harmonic. Conversely, we exhibit a representation of minimal surfaces in Anti-de Sitter space in terms of a given harmonic map.

• 出版日期2011-3