| 摘要: |
| 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. |
| 关键词: 弱B对称流形 2阶爱因斯坦流形 拟爱因斯坦流形 1-形式 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:国家自然科学基金资助 (12061014); 广西自然科学基金项目资助 (2019GXNSFAA245043). |
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| WEAKLY B SYMMETRIC MANIFOLDS |
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HUANG Zhi-ming, GAN Li-ning, LU Wei-jun
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School of Mathematics and Physics, Guangxi Minzu University, Nanning 530006, China
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| Abstract: |
| In this paper, we study some geometric properties of a special symmetric manifolds(weakly B-symmetric manifolds, denoted by (WBS)n). By using the symmetry of B tensor, we obtain a sufficient condition for (WBS)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 and ω is closed, respectively. Then we study Einstein (WBS)n (n > 2). Finally, we construct an example of (WBS)4 manifold. |
| Key words: weakly B symmetric manifolds Einstein manifolds of level 2 quasi-Einstein manifolds one-forms |
