The space of Lorentzian flat tori in anti-de Sitter 3-space

Details The space of Lorentzian flat tori in anti-de Sitter 3-space The space of Lorentzian flat tori in anti-de Sitter 3-space

2009-05-25

arxiv.org/abs/0905.3991v1

Mathematics

Differential Geometry

30 pages

Scientific paper

We describe the space of isometric immersions from the Lorentz plane $L^2$ into the 3-dimensional anti-de Sitter space, and solve several open problems of this context raised by M. Dajczer and K. Nomizu in 1981. We also obtain from the above result a description of the space of Lorentzian flat tori isometrically immersed in the anti de Sitter space in terms of pairs of closed curves with wave front singularities in the hyperbolic plane satisfying some compatibility conditions.

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