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On Compact Riemannian Manifolds with Harmonic Weyl Curvature

  • Hai-Ping Fu
  • Hui-Ya HeEmail author
Article
  • 16 Downloads

Abstract

We give some rigidity theorems for an n-dimensional (\(n\ge 4\)) compact Riemannian manifold with harmonic Weyl curvature, positive scalar curvature and positive constant \(\sigma _2\) curvature. Moreover, we prove that a 4-dimensional compact locally conformally flat Riemannian manifold with positive scalar curvature and positive constant \(\sigma _2\) curvature is isometric to a quotient of the round \(\mathbb {S}^4\).

Keywords

Einstein manifold harmonic Weyl curvature Schouten tensor 

Mathematics Subject Classification

Primary 53C21 Secondary 53C20 

Notes

Acknowledgements

The authors are very grateful to Professor Haizhong Li for his guidance and constant support.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsNanchang UniversityNanchangPeople’s Republic of China
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingPeople’s Republic of China

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