4-dimensional compact manifolds with nonnegative biorthogonal curvature

2013/11/05 by Ezio Costa, Costa, E., E. Ribeiro +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1311.1057

openalex publication_date 2013/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Sectional Curvature, Isotropic Curvature, and Yau's Pinching Problem

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