弱B对称流形

WEAKLY B SYMMETRIC MANIFOLDS

本文研究了一类特殊的对称流形(弱B对称流形,简记(WBS)n)的几何性质问题.利用B张量的对称性,获得了(WBS)n是一个2阶爱因斯坦流形的充分条件并证明这个流形是拟爱因斯坦流形.根据指标的轮换,分别获得了1-形式K和ω是闭形式的充要条件,继而考虑满足爱因斯坦度量条件的(WBS)_(n)(n>2).最后给出一个(WBS)_(4)的例子.

In this paper,we study some geometric properties of a special symmetric manifolds(weakly B-symmetric manifolds,denoted by(W BS)n).By using the symmetry of B tensor,we obtain a sufficient condition for(W BS)n to be an Einstein manifold of level 2 and prove that such manifold is a quasi-Einstein manifold.According to the method of index rotation,we obtain a necessary and sufficient condition for 1-forms K andωis closed,respectively.Then we study Einstein(W BS)_(n)(n>2).Finally,we construct an example of(W BS)_(4) manifold.