Quaternionic-K\"ahler manifolds with nonnegative sectional curvature

TL;DR

This paper proves that compact quaternionic-Kähler manifolds with positive scalar curvature and nonnegative sectional curvature are symmetric spaces, extending Berger's classical theorem and deepening understanding of their geometric structure.

Contribution

It extends Berger's classical theorem by showing such manifolds are isometric to symmetric spaces under specified curvature conditions.

Findings

Manifolds are isometric to symmetric spaces

Extension of Berger's theorem to new curvature conditions

Characterization of quaternionic-Kähler manifolds with specific curvature

Abstract

We show that a compact quaternionic-K\"ahler manifold with positive scalar curvature and nonnegative sectional curvature is isometric to a symmetric space. This extends a classical theorem of Berger.