Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor

Details Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor

2007-12-09

arxiv.org/abs/0712.1321v2

J. Geom. Phys., Volume 60, Issue 3, March 2010, 477-490

Mathematics

Differential Geometry

Correction to one of the examples

Scientific paper

10.1016/j.geomphys.2009.11.001

We consider the Hawking-Penrose singularity theorems and the Lorentzian
splitting theorem under the weaker curvature condition of nonnegative
Bakry-Emery-Ricci curvature $Ric_f^m$ in timelike directions. We prove that
they still hold when $m$ is finite, and when $m$ is infinite, they hold under
the additional assumption that $f$ is bounded from above.

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