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Maximal spacelike surfaces in a certain homogeneous Lorentzian 3-manifold

Abstract

The 2-parameter family of certain homogeneous Lorentzian 3-manifolds, which includes Minkowski 3-space and anti-de Sitter 3-space, is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral representation formula for maximal spacelike surfaces in the homogeneous Lorentzian 3-manifolds is obtained. The normal Gauß map of maximal spacelike surfaces and its harmonicity are discussed.

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Notes

  1. 1.

    From here on we mean a surface by an immersion.

  2. 2.

    It can be also obtained directly from (14).

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Correspondence to Sungwook Lee.

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Lee, S. Maximal spacelike surfaces in a certain homogeneous Lorentzian 3-manifold. J. Geom. 112, 27 (2021). https://doi.org/10.1007/s00022-021-00591-6

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Keywords

  • Anti-de Sitter space
  • harmonic map
  • homogeneous manifold
  • Lorentzian manifold
  • maximal surface
  • Minkowski space
  • spacelike surface
  • solvable Lie group

Mathematics Subject Classification

  • 53A10
  • 53C30
  • 53C42
  • 53C50