Geometric analysis of Lorentzian distance function on spacelike hypersurfaces
Differential Geometry
2009-02-16 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.0802.4376,
title = {Geometric analysis of Lorentzian distance function on spacelike hypersurfaces},
author = {Luis J. Alias and Ana Hurtado and Vicente Palmer},
journal= {arXiv preprint arXiv:0802.4376},
year = {2009}
}
Comments
Final version (January 2009). To appear in the Transactions of the American Mathematical Society