A general Schwarz lemma for almost-Hermitian manifolds

We prove a version of Yau's Schwarz lemma for general almostcomplex manifolds equipped with almost-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 almost- Hermitian metric with bisectional curvature bounded between two negative constants that satisfies some additional assumptions.

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Published 1 January 2007