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arXiv · 0712.1321

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

Jeffrey S. Case
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Abstract

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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Jeffrey S. Case. 2008-06-03. Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor. https://doi.org/10.1016/j.geomphys.2009.11.001

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