1995/11/23 by Akhil Ranjan, Ranjan, Akhil, G. Santhanam +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.dg-ga/9511010
In a complete Riemannian manifold (M, g) if the hessian of a real valued function satisfies some suitable conditions then it restricts the geometry of (M, g). In this paper we characterize all compact rank-1 symmetric spaces, as those Riemannian manifolds (M, g) admitting a real valued function u such that the hessian of u has atmost two eigenvalues -u and -u+1\over 2, under some mild hypothesis on (M, g). This generalises a well known result of Obata which characterizes all round spheres.