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
From here on we mean a surface by an immersion.
It can be also obtained directly from (14).
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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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DOI: https://doi.org/10.1007/s00022-021-00591-6
Keywords
- Anti-de Sitter space
- harmonic map
- homogeneous manifold
- Lorentzian manifold
- maximal surface
- Minkowski space
- spacelike surface
- solvable Lie group