A Lichnerowicz–Obata–Cheng Type Theorem on Finsler Manifolds

Songting Yin and Pan Zhang
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Songting Yin: Department of Mathematics and Computer Science, Tongling University, Tongling 244000, China
Pan Zhang: School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

Mathematics, 2018, vol. 6, issue 12, 1-7

Abstract: 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.

Keywords: the first eigenvalue; Ricci curvature; S-curvature; Finsler sphere (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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