局部共形对称黎曼流形的孤立现象

Isolation Phenomena for the Locally Conformal Symmetric Riemannian Manifold

讨论了局部共形对称的封闭黎曼流形,证明了黎曼曲率张量模长的一个拼挤定理.当M是局部共形平坦流形时,得到了曲率张量模长的最佳拼挤常数,并确定了达到该值的黎曼流形.

We study the locally conformally symmetric closed Riemannian Manifolds,and establish a pinching theorem for the square of the length of the Riemannian curvature vector.When M is a locally conformally fiat Riemannian manifold,we obtain the best pinching constant for curvature vector and determine the manifold with this constant.