A general Schwarz Lemma for almost-Hermitian manifolds
Differential Geometry
2014-01-21 v3
Abstract
We prove a version of Yau's Schwarz Lemma for general almost-complex manifolds equipped with Hermitian metrics. This requires an extension to this setting of the Laplacian comparison theorem. As an application we show that the product of two almost-complex manifolds does not admit any complete Hermitian metric with bisectional curvature bounded between two negative constants that satisfies some additional mild assumptions.
Keywords
Cite
@article{arxiv.0707.0527,
title = {A general Schwarz Lemma for almost-Hermitian manifolds},
author = {Valentino Tosatti},
journal= {arXiv preprint arXiv:0707.0527},
year = {2014}
}
Comments
21 pages; v2 added some remarks and references; v3 fixed typos, final version to appear in Communications in Analysis and Geometry