Compact K\"ahler manifolds with positive orthogonal bisectional curvature

TL;DR

This paper provides a new proof that compact Kähler manifolds with positive orthogonal bisectional curvature are biholomorphic to complex projective space, using Siu-Yau's method.

Contribution

It introduces a novel proof technique for classifying such manifolds, simplifying previous approaches and confirming their biholomorphic equivalence to projective space.

Findings

Any n-dimensional compact Kähler manifold with positive orthogonal bisectional curvature is biholomorphic to p^n.

The proof employs Siu-Yau's method to establish the classification.

The result confirms the geometric rigidity of these manifolds.

Abstract

In this short note, using Siu-Yau's method [14], we give a new proof that any n-dimensional compact Kahler manifold with positive orthogonal bisectional curvature must be biholomorphic to $\mathbb{P}^n$.