Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below

2018 ◽  
Vol 13 (2) ◽  
pp. 435-448 ◽  
Author(s):  
Songting Yin
Keyword(s):  
Ricci Curvature ◽  
Comparison Theorems ◽  
Finsler Manifolds ◽  
Weighted Ricci Curvature ◽  
Bounded Below

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 A Note on Finsler Version of Calabi-Yau Theorem

2018 ◽  
Vol 2018 ◽  
pp. 1-4
Author(s):  
Songting Yin ◽  
Ruixin Wang ◽  
Pan Zhang
Keyword(s):  
Ricci Curvature ◽  
Volume Growth ◽  
Finsler Manifold ◽  
Infinite Volume ◽  
Growth Theorem ◽  
Negative Function ◽  
Weighted Ricci Curvature ◽  
Bounded Below

We generalize Calabi-Yau’s linear volume growth theorem to Finsler manifold with the weighted Ricci curvature bounded below by a negative function and show that such a manifold must have infinite volume.

scholarly journals A Lichnerowicz–Obata–Cheng Type Theorem on Finsler Manifolds

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 311
Author(s):  
Songting Yin ◽  
Pan Zhang
Keyword(s):  
Lower Bound ◽  
Ricci Curvature ◽  
Distance Function ◽  
Type Theorem ◽  
Finsler Manifold ◽  
First Eigenvalue ◽  
Comparison Result ◽  
Finsler Manifolds ◽  
The First Eigenvalue ◽  
Bounded Below

Let ( M , F , d μ ) be a Finsler manifold with the Ricci curvature bounded below by a positive number and constant S-curvature. We prove that, if the first eigenvalue of the Finsler–Laplacian attains its lower bound, then M is isometric to a Finsler sphere. Moreover, we establish a comparison result on the Hessian trace of the distance function.

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