A Lichnerowicz-Obata-Cheng type theorem on Finsler manifolds (Q2337274)

Summary: Let \((M, F, d \mu)\) 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.