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Open AccessArticle

A Lichnerowicz–Obata–Cheng Type Theorem on Finsler Manifolds

by Songting Yin 1 and Pan Zhang 2,*
1
Department of Mathematics and Computer Science, Tongling University, Tongling 244000, China
2
School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 311; https://doi.org/10.3390/math6120311
Received: 29 October 2018 / Revised: 1 December 2018 / Accepted: 6 December 2018 / Published: 7 December 2018
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. View Full-Text
Keywords: the first eigenvalue; Ricci curvature; S-curvature; Finsler sphere the first eigenvalue; Ricci curvature; S-curvature; Finsler sphere
MDPI and ACS Style

Yin, S.; Zhang, P. A Lichnerowicz–Obata–Cheng Type Theorem on Finsler Manifolds. Mathematics 2018, 6, 311.

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