Classification of manifolds with weakly 1/4-pinched curvatures

TL;DR

This paper proves that compact Riemannian manifolds with weakly 1/4-pinched sectional curvatures are either locally symmetric or space forms, clarifying their geometric classification.

Contribution

It establishes a classification theorem for manifolds with weakly 1/4-pinched curvatures, extending previous results to this curvature condition.

Findings

Manifolds with weakly 1/4-pinched curvatures are either locally symmetric or space forms.

Provides a geometric classification based on curvature pinching conditions.

Enhances understanding of curvature conditions in Riemannian geometry.

Abstract

We show that a compact Riemannian manifold with weakly 1/4-pinched sectional curvatures is either locally symmetric or diffeomorphic to a space form.