Sasaki联络的高维推广

The Higher Dimensional Generalization of Sasaki Connection

本篇论文简单介绍了Shchepetilov定义的Sasaki联络▽X和类似于Sasaki联络的联络▽aX,并计算了联络▽aX的数量曲率,截面曲率和测地线.再将两个联络分别推广到高维情况,并计算了一些相应的几何结果.

In this paper,the Sasaki connection ▽X defined by Shchepetilov and the similar Sasaki connection ▽aX on warped product spaces are diucussed and section curvature,scalar curvature,and geodesic on ▽aX are calculated.Meanwhile,the higher dimensional generalization of the two connections are given,and some geometric results are proved.