一类具有调和曲率黎曼流形刚性定理的推广

Generalization of a class of rigidity theorem for Riemannian manifolds with harmonic curvature

通过建立任意黎曼流形零迹黎曼曲率张量模长平方的拉普拉斯公式,在具有平行Cotton张量、正Sobolev常数和负数量曲率的条件下,证明了完备非紧黎曼流形的一个刚性定理,推广了相关结果。

In this paper,by establishing the Laplacian of the norm square of the trace-free curvature tensor for any Riemannian manifold,a rigidity theorem for complete noncompact Riemannian manifold with parallel Cotton tensor,positive Sobolev constant and negative scalar curvature was prvoed,which extends the corresponding results.