Bull. Korean Math. Soc. 2019; 56(5): 1341-1353
Online first article August 6, 2019 Printed September 30, 2019
https://doi.org/10.4134/BKMS.b181193
Copyright © The Korean Mathematical Society.
Guangyue Huang, Bingqing Ma
Henan Normal University; Henan Normal University
For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.
Keywords: Sobolev constant, rigidity, vanishing Bach tensor
MSC numbers: Primary 53C24; Secondary 53C21
Supported by: The research of the rst author is supported by NSFC(Nos. 11371018, 11671121) and the second author is supported by NSFC(No. 11401179).
2022; 59(2): 351-360
2020; 57(6): 1367-1382
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2013; 50(1): 135-142
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