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

被引：54

作者：

Case, Jeffrey S. ^{[1
]}

机构：

[1] Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2010年 / 60卷 / 03期

关键词：

Bakry-Emery tensor; Singularity theorems; Lorentzian splitting theorems; CURVATURE; REGULARITY; SURFACES;

D O I：

10.1016/j.geomphys.2009.11.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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) timelike directions. We prove that they still hold when in is finite, and when m is infinite, they hold under the additional assumption that f is bounded from above. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：477 / 490

页数：14

共 47 条

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[35] Myers’ Type Theorem for Integral Bakry–Émery Ricci Tensor Bounds
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[36] Some Almost-Schur type inequalities for k-Bakry-Emery Ricci tensor
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[38] Stable weighted minimal surfaces in manifolds with non-negative Bakry-Emery Ricci tensor
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