A general Schwarz Lemma for almost-Hermitian manifolds

Details A general Schwarz Lemma for almost-Hermitian manifolds A general Schwarz Lemma for almost-Hermitian manifolds

2007-07-04

arxiv.org/abs/0707.0527v3

Comm. Anal. Geom. 15 (2007), no.5, 1063-1086.

Mathematics

Differential Geometry

21 pages; v2 added some remarks and references; v3 fixed typos, final version to appear in Communications in Analysis and Geom

Scientific paper

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.

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