Einstein four-manifolds of pinched sectional curvature

TL;DR

This paper classifies four-dimensional Einstein manifolds with positive Ricci curvature under pinched sectional curvature conditions, improving existing bounds and generalizing previous results.

Contribution

It provides new classification results for Einstein four-manifolds with pinched curvature, refining bounds and extending prior theorems.

Findings

Established an upper bound for sectional curvature, improving Costa's theorem.

Generalized Yang's result by assuming an upper bound on the difference between sectional curvatures.

Enhanced understanding of curvature constraints in Einstein four-manifolds.

Abstract

In this paper, we obtain classification of four-dimensional Einstein manifolds with positive Ricci curvature and pinched sectional curvature. In particular, the first result concerns with an upper bound of sectional curvature, improving a theorem of E. Costa. The second is a generalization of D. Yang's result assuming an upper bound on the difference between sectional curvatures.