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RIGIDITY CHARACTERIZATIONS OF COMPLETE RIEMANNIAN MANIFOLDS WITH α-BACH-FLAT

  • Huang, Guangyue (College of Mathematics and Information Science Henan Normal University) ;
  • Zeng, Qianyu (College of Mathematics and Information Science Henan Normal University)
  • Received : 2020.02.17
  • Accepted : 2020.06.05
  • Published : 2021.03.01

Abstract

For complete manifolds with α-Bach tensor (which is defined by (1.2)) flat, we provide some rigidity results characterized by some point-wise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moveover, some Einstein metrics have also been characterized by some $L^{\frac{n}{2}}$-integral inequalities. Furthermore, we also give some rigidity characterizations for constant sectional curvature.