拟常曲率空间的高维曲率特征

A CHARACTERIZATION OF SPACES OF QUASI-CONSTANT CURVATURE BY THE CURVATURE IN m-DIRECTION

利用Cartan引进的仔意维方向上的曲率的概念，证明了拟常由率空间和拟爱因斯坦空间的高维曲率特征。并得出常肉率空间和爱因斯坦空间的相应特征，因而对Fedishenko和Chernyshenko的猜想作出肯定的回答。

By means of Cartan's concept of the curvature in an m-direction,some new characterizations for spaces of quasi-constant curvature and quasi-Einstein spaces are obtained. Corresponding results for spaces of constant curvature and for Einstein spaces are also given, which affirmatively answer the conjectures of Fedishenko and Chernyshenko.