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arXiv · 0707.0527

A general Schwarz Lemma for almost-Hermitian manifolds

Valentino Tosatti
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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.

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BibTeXRIS

Valentino Tosatti. 2007-09-19. A general Schwarz Lemma for almost-Hermitian manifolds. https://doi.org/10.4310/cag.2007.v15.n5.a6

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