K\"ahler C-spaces and quadratic bisectional curvature

TL;DR

This paper establishes conditions for certain irreducible Kähler C-spaces to have nonnegative or positive quadratic bisectional curvature, using computational tools for exceptional Lie groups, and relates findings to existing conjectures.

Contribution

It provides necessary and sufficient conditions for quadratic bisectional curvature in irreducible Kähler C-spaces with b_2=1, especially for exceptional Lie groups, advancing understanding in differential geometry.

Findings

Conditions for nonnegative quadratic bisectional curvature

Conditions for positive quadratic bisectional curvature

Verification of conjectures for exceptional Lie groups

Abstract

In this article we give necessary and sufficient conditions for an irreducible K\"ahler C-space with $b_2=1$ to have nonnegative or positive quadratic bisectional curvature, assuming the space is not Hermitian symmetric. In the cases of the five exceptional Lie groups $E_6, E_7, E_8, F_4, G_2$, the computer package MAPLE is used to assist our calculations. The results are related to two conjectures of Li-Wu-Zheng.