scholarly journals The splitting theorem and topology of noncompact spaces with nonnegative $N$-Bakry Émery Ricci curvature

2020 ◽  
pp. 1
Author(s):  
Alice Lim
Keyword(s):  
Ricci Curvature ◽  
Splitting Theorem ◽  
And Topology

scholarly journals Splitting theorems for Finsler manifolds of nonnegative Ricci curvature

2015 ◽  
Vol 2015 (700) ◽  
Author(s):  
Shin-ichi Ohta
Keyword(s):  
Vector Field ◽  
Ricci Curvature ◽  
Splitting Theorem ◽  
Gradient Vector ◽  
Busemann Function ◽  
Finsler Manifolds ◽  
Nonnegative Ricci Curvature ◽  
Straight Line ◽  
Weighted Ricci Curvature ◽  
Gradient Vector Field

AbstractWe investigate the structure of a Finsler manifold of nonnegative weighted Ricci curvature including a straight line, and extend the classical Cheeger–Gromoll–Lichnerowicz Splitting Theorem. Such a space admits a diffeomorphic, measure-preserving splitting in general. As for a special class of Berwald spaces, we can perform the isometric splitting in the sense that there is a one-parameter family of isometries generated from the gradient vector field of the Busemann function. A Betti number estimate is also given for Berwald spaces.

scholarly journals On a theorem of Ambrose

2006 ◽  
Vol 81 (2) ◽  
pp. 149-152 ◽  
Author(s):  
David J. Wraith
Keyword(s):  
Ricci Curvature ◽  
Alternative Proof ◽  
And Topology ◽  
Riccati Inequality ◽  
Topology Of Manifolds

AbstractA Riccati inequality involving the Ricci curvature can be used to deduce many interesting results about the geometry and topology of manifolds. In this note we use it to present a short alternative proof to a theorem of Ambrose.

scholarly journals Two generalizations of Cheeger-Gromoll splitting theorem via Bakry-Emery Ricci curvature

2009 ◽  
Vol 59 (2) ◽  
pp. 563-573 ◽  
Author(s):  
Fuquan Fang ◽  
Xiang-Dong Li ◽  
Zhenlei Zhang
Keyword(s):  
Ricci Curvature ◽  
Splitting Theorem

scholarly journals The splitting theorem for manifolds of nonnegative Ricci curvature

1971 ◽  
Vol 6 (1) ◽  
pp. 119-128 ◽  
Author(s):  
Jeff Cheeger ◽  
Detlef Gromoll
Keyword(s):  
Ricci Curvature ◽  
Splitting Theorem ◽  
Nonnegative Ricci Curvature

ON INTEGRAL RICCI CURVATURE AND TOPOLOGY OF FINSLER MANIFOLDS

2012 ◽  
Vol 23 (11) ◽  
pp. 1250111 ◽  
Author(s):  
B. Y. WU
Keyword(s):  
Ricci Curvature ◽  
Comparison Theorem ◽  
Relative Volume ◽  
Volume Form ◽  
Finsler Manifolds ◽  
Volume Comparison ◽  
Minimal Volume ◽  
Curvature Bound ◽  
And Topology

We establish a relative volume comparison theorem for minimal volume form of Finsler manifolds under integral Ricci curvature bound. As its applications, we obtain some results on integral Ricci curvature and topology of Finsler manifolds. These results generalize the corresponding properties with pointwise Ricci curvature bound in the literatures.

Sign in / Sign up

Export Citation Format

Share Document