In this work, we show that semi-Riemannian group manifold admits Ricci solitons and satisfies the dynamical cosmology equation of spacetime. In Sec. 2, we introduce and provide some geometric properties of semisymmetric nonmetric connection in semi-Riemannian space. In Sec. 3, we define and show some geometric properties of group manifold endowed with semisymmetric nonmetric connection in semi-Riemannian space. In the section that follows, we give a condition of a group manifold to be Ricci solitons and gradient Ricci soliton. In Sec. 5, we provide the applications of group manifold admitting Ricci solitons in the theory of general relativity.

中文翻译：

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半黎曼群流形的几何及其在时空中接纳里奇孤子的应用

在这项工作中，我们证明了半黎曼群流形承认 Ricci 孤子并满足时空的动力宇宙学方程。在秒。2，我们介绍并提供了半对称非度量连接在半黎曼空间中的一些几何性质。在秒。3，我们定义并展示了在半黎曼空间中具有半对称非度量连接的群流形的一些几何性质。在接下来的部分中，我们给出一个群流形的条件是里奇孤子和梯度里奇孤子。在秒。5、我们提供了接纳里奇孤子的群流形在广义相对论中的应用。