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Mathematics > Differential Geometry

arXiv:0712.1321 (math)
[Submitted on 9 Dec 2007 (v1), last revised 3 Jun 2008 (this version, v2)]

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

Authors: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.
Comments: Correction to one of the examples
Subjects: Differential Geometry (math.DG)
MSC classes: 53C50, 83C75
Cite as: arXiv:0712.1321 [math.DG]
  (or arXiv:0712.1321v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0712.1321
Journal reference: J. Geom. Phys., Volume 60, Issue 3, March 2010, 477-490
Related DOI: https://doi.org/10.1016/j.geomphys.2009.11.001

Submission history

From: Jeffrey Case [view email]
[v1] Sun, 9 Dec 2007 20:40:58 UTC (17 KB)
[v2] Tue, 3 Jun 2008 05:51:34 UTC (18 KB)
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