We prove a version of Yau's Schwarz lemma for general almost-complex 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.
ASJC Scopus subject areas
- Statistics and Probability
- Geometry and Topology
- Statistics, Probability and Uncertainty