A generalized Frankel conjecture via the Yang-Mills flow

TL;DR

This paper introduces a new curvature condition called 2-positive bisectional curvature on compact Kähler manifolds, providing a characterization theorem that extends classical results like the Frankel conjecture.

Contribution

It defines a novel curvature condition and proves a characterization theorem for manifolds satisfying this condition, extending classical geometric conjectures.

Findings

Characterization theorem for 2-positive bisectional curvature manifolds

Extension of the Frankel conjecture to new curvature conditions

New insights into the geometry of compact Kähler manifolds

Abstract

In this note, we introduce a new curvature condition called the $2-$positive bisectional curvature on compact K\"{a}hler manifolds. We then deduce a characterization theorem for manifolds with $2-$positive bisectional curvature, which can be regarded as a variant of the classical Frankel conjecture (cf.\cite{Fra61,SY80}) and its generalizations (cf.\cite{Siu80,Mok88}).