弱B对称流形OACSTPCD
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(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(WBSS)4 manifold.
黄志明;甘丽宁;卢卫君
广西民族大学数学与物理学院,广西南宁 530006
数学
弱B对称流形2阶爱因斯坦流形拟爱因斯坦流形1-形式
weakly B symmetric manifoldsEinstein manifolds of level 2quasi-Einstein manifoldsone-forms
《数学杂志》 2024 (002)
141-156 / 16
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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