Proof of the Yano-Obata Conjecture for holomorph-projective transformations

Abstract

We prove the classical Yano-Obata conjecture by showing that the connected component of the group of holomorph-projective transformations of a closed, connected Riemannian Kähler manifold consists of isometries unless the metric has constant positive holomorphic curvature.

28 pages, 3 pictures. The (v2) version contains in addition a relation between h-projectively equivalent metrics and hamiltonian 2-forms studies in math.DG/0202280, math.DG/0401320, math.DG/0511118, math.DG/0511119. In the (v3) version, we also added an appendix with the h-projectively invariant formulation of the main equations and, as their application, an alternative proof of Lemma 7

References in corpus (1)

• Closed manifolds admitting metrics with the same geodesics

Cited by in corpus (2)

• C-projective geometry
• Quantum integrability for the Beltrami-Laplace operators of projectively equivalent metrics of arbitrary signatures