Diameter rigidity for Kahler manifolds with positive bisectional curvature

TL;DR

This paper proves that Kahler manifolds with positive bisectional curvature and maximal diameter are isometric to complex projective space with the Fubini-Study metric, establishing a diameter rigidity result.

Contribution

It establishes a diameter rigidity theorem for Kahler manifolds with positive bisectional curvature, characterizing them as complex projective spaces.

Findings

Kahler manifolds with positive bisectional curvature and maximal diameter are isometric to complex projective space.

The Fubini-Study metric uniquely characterizes the maximal diameter case.

The result extends classical rigidity theorems to the Kahler setting.

Abstract

We prove that a Kahler manifold with positive bisectional curvature and maximal diameter is isometric to the complex projective space with the Fubini-Study metric.