scholarly journals An Extension Theorem for Weighted Ricci Curvature on Finsler Manifolds

2019 ◽  
Vol 40 (4) ◽  
pp. 867-874
Author(s):  
Yasemin Soylu
Keyword(s):  
Ricci Curvature ◽  
Extension Theorem ◽  
Finsler Manifolds ◽  
Weighted Ricci Curvature

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.

Weighted Ricci Curvature

2021 ◽  
pp. 115-128
Author(s):  
Shin-ichi Ohta
Keyword(s):  
Ricci Curvature ◽  
Weighted Ricci Curvature

SOME RESULTS ON FUNDAMENTAL GROUPS AND BETTI NUMBERS OF FINSLER MANIFOLDS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250063 ◽  
Author(s):  
YIBING SHEN ◽  
WEI ZHAO
Keyword(s):  
Ricci Curvature ◽  
Betti Number ◽  
Betti Numbers ◽  
Finsler Manifold ◽  
Fundamental Groups ◽  
Finsler Manifolds ◽  
Nonnegative Ricci Curvature ◽  
Finiteness Theorems ◽  
The Relationship

In this paper the relationship between the Ricci curvature and the fundamental groups of Finsler manifolds are studied. We give an estimate of the first Betti number of a compact Finsler manifold. Two finiteness theorems for fundamental groups of compact Finsler manifolds are proved. Moreover, the growth of fundamental groups of Finsler manifolds with almost-nonnegative Ricci curvature are considered.

Sign in / Sign up

Export Citation Format

Share Document