Open AccessSome rigidity theorems on Finsler manifolds
Author(s) -
Songting Yin
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021184
Subject(s) - mathematics , rigidity (electromagnetism) , finsler manifold , ricci curvature , bounded function , laplace operator , pure mathematics , eigenvalues and eigenvectors , upper and lower bounds , closed manifold , manifold (fluid mechanics) , mathematical analysis , curvature , riemannian manifold , geometry , invariant manifold , physics , mechanical engineering , quantum mechanics , engineering
We prove that, for a Finsler manifold with the weighted Ricci curvature bounded below by a positive number, it is a Finsler sphere if and only if the diam attains its maximal value, if and only if the volume attains its maximal value, and if and only if the first closed eigenvalue of the Finsler-Laplacian attains its lower bound. These generalize some rigidity theorems in Riemannian geometry to the Finsler setting.