PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Noncompact complete manifolds with cyclic parallel Ricci curvature

Volume 119 / 2017

Yawei Chu Annales Polonici Mathematici 119 (2017), 95-105 MSC: Primary 53C24; Secondary 53C20. DOI: 10.4064/ap4123-3-2017 Published online: 11 July 2017


Let $(M^n,g)$ be a noncompact complete $n$-dimensional Riemannian manifold with cyclic parallel Ricci curvature and positive Yamabe constant. When the scalar curvature $R$ is negative, assuming that the $L^\beta $-norms (see Theorem 1.1 for the range of $\beta $) of the Weyl curvature are finite, we show that $(M^n,g)$ is a space form if $n\ge 7$ and the $L^{n/2}$-norms of the traceless Ricci curvature and Weyl curvature are small enough. When $R=0,$ the same rigidity result is also obtained for all dimensions $n\ge 3$ without the assumption on the $L^\beta $-norms of the Weyl curvature.


  • Yawei ChuSchool of Mathematics and Statistics
    Fuyang Normal University
    Fuyang, 236037, People’s Republic of China
    College of Information Engineering
    Fuyang Normal University
    Fuyang, 236041, People’s Republic of China

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image