Geometry of semi-Riemannian group manifold and its applications in spacetime admitting Ricci solitons

Abstract

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.