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

Research output: Contribution to journal › Article › peer-review

67 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
General Physics and Astronomy
Geometry and Topology

Access to Document

10.1016/j.geomphys.2009.11.001

Cite this

@article{1447c9c3e70f45b7871bbfbffdc48af4,

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.",

author = "Case, \{Jeffrey S.\}",

year = "2010",

month = mar,

doi = "10.1016/j.geomphys.2009.11.001",

language = "English (US)",

volume = "60",

pages = "477--490",

journal = "Journal of Geometry and Physics",

issn = "0393-0440",

publisher = "Elsevier B.V.",

number = "3",

}

TY - JOUR

T1 - Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor

AU - Case, Jeffrey S.

PY - 2010/3

Y1 - 2010/3

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.

UR - https://www.scopus.com/pages/publications/75749141629

UR - https://www.scopus.com/pages/publications/75749141629#tab=citedBy

U2 - 10.1016/j.geomphys.2009.11.001

DO - 10.1016/j.geomphys.2009.11.001

M3 - Article

AN - SCOPUS:75749141629

SN - 0393-0440

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

Access to Document

Other files and links

Fingerprint

Cite this