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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).

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