Proof of the Yano-Obata conjecture for $h$-projective transformations

Abstract

We prove the classical Yano-Obata conjecture by showing that the connected component of the group of $h$-projective transformations of a closed, connected Riemannian Kähler manifold consists of isometries unless the manifold is the complex projective space with the standard Fubini-Study metric (up to a constant).