A general Schwarz Lemma for almost-Hermitian manifolds

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.

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

References in corpus (1)

• Taming symplectic forms and the Calabi-Yau equation

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