On quadratic orthogonal bisectional curvature

TL;DR

This paper investigates compact Kähler manifolds with specific nonnegative bisectional curvature conditions, establishing results on scalar curvature, Chern class positivity, and decompositions of the universal cover, contributing to their geometric classification.

Contribution

It provides new insights into the curvature properties and structural decompositions of Kähler manifolds under nonnegativity conditions on bisectional curvature.

Findings

Scalar curvature is nonnegative under the condition.

First Chern class is positive if the manifold is locally irreducible.

Partial classification of de Rham decompositions of the universal cover.

Abstract

In this article we study compact K\ahler manifolds satisfying a certain nonnegativity condition on the bisectional curvature. Under this condition, we show that the scalar curvature is nonnegative and that the first Chern class is positive assuming local irreducibility. We also obtain a partial classification of possible de Rham decompositions of the universal cover under this condition