4-dimensional compact manifolds with nonnegative biorthogonal curvature

E. Costa; E. Ribeiro

4-dimensional compact manifolds with nonnegative biorthogonal curvature

Differential Geometry 2014-03-28 v3

Authors: E. Costa , E. Ribeiro

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.

Keywords

4-dimensional compact manifolds nonnegative biorthogonal curvature pinching problem Yau Conjecture Riemannian manifolds sectional curvature classification

Cite

@article{arxiv.1311.1057,
  title  = {4-dimensional compact manifolds with nonnegative biorthogonal curvature},
  author = {E. Costa and E. Ribeiro},
  journal= {arXiv preprint arXiv:1311.1057},
  year   = {2014}
}

Comments

To appear in the Michigan Mathematical Journal

4-dimensional compact manifolds with nonnegative biorthogonal curvature

Abstract

Keywords

Cite

Comments

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