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arXiv · 1202.4589

On spacelike surfaces in 4-dimensional Lorentz-Minkowski spacetime through a lightcone

Francisco J. Palomo·Alfonso Romero
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Abstract

On any spacelike surface in a lightcone of four dimensional Lorentz-Minkowski space a distinguished smooth function is considered. It is shown how both extrinsic and intrinsic geometry of such a surface is codified by this function. The existence of a local maximum is assumed to decide when the spacelike surface must be totally umbilical, deriving a Liebmann type result. Two remarkable families of examples of spacelike surfaces in a lightcone are explicitly constructed. Finally, several results which involve the first eigenvalue of the Laplace operator of a compact spacelike surface in a lightcone are obtained.

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Francisco J. Palomo, Alfonso Romero. 2012-02-21. On spacelike surfaces in 4-dimensional Lorentz-Minkowski spacetime through a lightcone. https://arxiv.org/abs/1202.4589

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