Almost Non-positive K\"{a}hler Manifolds

TL;DR

This paper demonstrates that compact Kähler manifolds with small positive sectional curvature have universal coverings that are contractible, revealing new geometric properties of such manifolds.

Contribution

It establishes a novel link between small positive sectional curvature and the contractibility of universal coverings in compact Kähler manifolds.

Findings

Universal coverings of certain Kähler manifolds are contractible.

Small positive sectional curvature implies topological simplicity.

Provides new insights into the geometry of Kähler manifolds.

Abstract

This paper proves that the universal covering of a compact K\"{a}hler manifold with small positive sectional curvature in a certain sense is contractible.