Proof of the Yano-Obata Conjecture for holomorph-projective transformations
Differential Geometry
2015-10-07 v3 Analysis of PDEs
Complex Variables
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 K\"ahler manifold consists of isometries unless the metric has constant positive holomorphic curvature.
Keywords
Cite
@article{arxiv.1103.5613,
title = {Proof of the Yano-Obata Conjecture for holomorph-projective transformations},
author = {Vladimir S. Matveev and Stefan Rosemann},
journal= {arXiv preprint arXiv:1103.5613},
year = {2015}
}
Comments
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