4-dimensional compact manifolds with nonnegative biorthogonal curvature

TL;DR

This paper investigates 4-dimensional compact manifolds with nonnegative biorthogonal curvature, providing classification results and partial answers to Yau's conjecture on pinching conditions.

Contribution

It introduces a study of biorthogonal curvature as a weaker condition than sectional curvature and classifies manifolds satisfying this condition in four dimensions.

Findings

Classification of 4D compact manifolds with nonnegative biorthogonal curvature

Partial resolution of Yau's pinching conjecture in 4D

Extension of curvature pinching concepts to biorthogonal curvature

Abstract

The goal of this article is to study the pinching problem proposed by S.-T. Yau in 1990 replacing sectional curvature by one weaker condition on biorthogonal curvature. Moreover, we classify 4-dimensional compact oriented Riemannian manifolds with nonnegative biorthogonal curvature. In particular, we obtain a partial answer to Yau Conjecture on pinching theorem for 4-dimensional compact manifolds.