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

Jeffrey S. Case

doi:10.1016/j.geomphys.2009.11.001

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

Jeffrey S. Case

Mathematics

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47 Scopus citations

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.

Original language	English (US)
Pages (from-to)	477-490
Number of pages	14
Journal	Journal of Geometry and Physics
Volume	60
Issue number	3
DOIs	https://doi.org/10.1016/j.geomphys.2009.11.001
State	Published - Mar 2010

All Science Journal Classification (ASJC) codes

Mathematical Physics
Physics and Astronomy(all)
Geometry and Topology

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10.1016/j.geomphys.2009.11.001

Cite this

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title = "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 Ricfm 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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AU - Case, Jeffrey S.

PY - 2010/3

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N2 - We consider the Hawking-Penrose singularity theorems and the Lorentzian splitting theorem under the weaker curvature condition of nonnegative Bakry-Emery-Ricci curvature Ricfm 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.

AB - We consider the Hawking-Penrose singularity theorems and the Lorentzian splitting theorem under the weaker curvature condition of nonnegative Bakry-Emery-Ricci curvature Ricfm 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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U2 - 10.1016/j.geomphys.2009.11.001

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M3 - Article

AN - SCOPUS:75749141629

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VL - 60

SP - 477

EP - 490

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

IS - 3

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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