局部共形平坦流形上的Schouten张量及其应用(英文)

A SCHOUTEN TENSOR ON THE LOCALLY CONFORMALLY FLAT MANIFOLD AND ITS APPLICATION

M是一个紧致的局部共形平坦黎曼流形,其上定义的Schouten张量是一个Codazzi张量.本文借助这个Codazzi张量引入Cheng和Yau的自伴算子,获得了局部共形平坦流形上的一些新的结果.

Consider a compact locally conformally flat Riemannian manifold M and dimension n ≥ 3. The Schouten tensor on M is a Codazzi tensor. In this paper, we introduce Cheng-Yau＇s self-adjoint operator □ for this Codazzi tensor and obtain some new results on locally conformally flat Riemannian manifold.