A general Schwarz Lemma for almost-Hermitian manifolds

By Valentino Tosatti. 2007

79 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9bc7dd78e7eced43e55a432c4ca2b8f8659de186

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Fang Zheng
2. Xiaokui Yang
3. Quanting Zhao
4. Valentino Tosatti
5. Lei Ni

In Geometry and Topology

1. Fang Zheng
2. Xiaokui Yang
3. Quanting Zhao
4. Valentino Tosatti
5. Lei Ni

Citations in the corpus

• On real bisectional curvature for Hermitian manifolds (2016, background): “There are also some Schwarz type inequalities in [16] under different curvature assumptions.”