Geometric analysis of Lorentzian distance function on spacelike hypersurfaces

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Some analysis on the Lorentzian distance in a spacetime with controlled sectional (or Ricci) curvatures is done. In particular, we focus on the study of the restriction of such distance to a spacelike hypersurface satisfying the Omori-Yau maximum principle. As a consequence, and under appropriate hypotheses on the (sectional or Ricci) curvatures of the ambient spacetime, we obtain sharp estimates for the mean curvature of those hypersurfaces. Moreover, we also give a suficient condition for its hyperbolicity.
Final version (January 2009). To appear in the Transactions of the American Mathematical Society

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Differential Geometry, Mathematical Physics, 53C50; 53C42; 31C05

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http://salesiana.dossiersoluciones.com/handle/123456789/219756

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0802.4376
 http://arxiv.org/abs/0802.4376

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arXiv