On compact Riemannian manifolds with harmonic weyl curvature

Haiping Fu; Huiya He

On compact Riemannian manifolds with harmonic weyl curvature

Differential Geometry 2018-10-17 v1

Authors: Haiping Fu , Huiya He

Abstract

We give some rigidity theorems for an n $(\geq4)$ -dimensional compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant $\sigma_2$ . Moreover, when $n=4,$ we prove that a 4-dimensional compact locally conformally flat Riemannian manifold with positive scalar curvature and positive constant $\sigma_2$ is isometric to a quotient of the round $\mathbb{S}^4$ .

Keywords

compact Riemannian manifold harmonic Weyl curvature positive scalar curvature sigma_2 rigidity theorem locally conformally flat isometric

Cite

@article{arxiv.1810.06301,
  title  = {On compact Riemannian manifolds with harmonic weyl curvature},
  author = {Haiping Fu and Huiya He},
  journal= {arXiv preprint arXiv:1810.06301},
  year   = {2018}
}

Comments

arXiv admin note: text overlap with arXiv:1512.00256

On compact Riemannian manifolds with harmonic weyl curvature

Abstract

Keywords

Cite

Comments

Related papers