Four-Dimensional Compact Manifolds with Nonnegative 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 a weaker condition on biorthogonal curvature.Moreover, we classify four-dimensional compact oriented Riemannian manifolds with nonnegative biorthogonal curvature.In particular, we obtain a partial answer to the Yau conjecture on pinching theorem for four-dimensional compact manifolds.