全纯射影变换的 Yano-Obata 猜想证明
微分几何
2015-10-07 v3 偏微分方程分析
复变函数
摘要
我们证明了经典的 Yano-Obata 猜想，证明了除非度量具有恒正全纯曲率，否则闭连通 Riemann Kähler 流形的全纯射影变换群的连通分支由等距构成。
引用
@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}
}
备注
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