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arXiv · 0802.4376

Geometric analysis of Lorentzian distance function on spacelike hypersurfaces

Luis J. Alias·Ana Hurtado·Vicente Palmer
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Abstract

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.

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BibTeXRIS

Luis J. Alias, Ana Hurtado, Vicente Palmer. 2009-02-16. Geometric analysis of Lorentzian distance function on spacelike hypersurfaces. https://arxiv.org/abs/0802.4376

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