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

Abstract

We consider the Hawking-Penrose singularity theorems and the Lorentzian splitting theorem under the weaker curvature condition of nonnegative Bakry-Emery-Ricci curvature $Ri{c}_f^m$ 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.

Correction to one of the examples

References in corpus (3)

• Comparison Geometry for the Bakry-Emery Ricci Tensor
• Some Geometric Properties of the Bakry-Emery-Ricci Tensor
• Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Émery Ricci curvature

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