2021/04/06 by Kaushik Chattopadhyay, Chattopadhyay, Kaushik, Arindam Bhattacharyya +3
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Cosmology and Gravitation Theories
paper · pdf · doi:10.48550/arxiv.2104.02501
In the present paper we discuss about a set of geometric properties and\nphysical applications of a mixed quasi-Einstein spacetime[M(QE)4], which\nis a special type of nearly quasi-Einstein spacetime[N(QE)4]. Firstly we\nconsider a nearly quasi-Einstein manifold[N(QE)n] along with a mixed\nquasi-Einstein manifold[M(QE)n] and study some geometric conditions with\nrespect to different curvature tensors on them. Then we consider a mixed\nquasi-Einstein spacetime and study W2-Ricci pseudosymmetry and projective\nRicci pseudosymmetry on it. Then we study the conditions H \⋅ S=0 and\n C \⋅ S=0 in an M(QE)4 spacetime, where H, C are the\nconharmonical curvature tensor and semiconformal curvature tensor respectively.\nNext we consider a semiconformally flat Ricci pseudosymmetric M(QE)4\nspacetime and find the nature of that spacetime. In the next section we study\nabout some applications of a perfect fluid M(QE)4 spacetime in the general\ntheory of relativity. Followed by we discuss about the Ricci soliton structure\nin a semiconformally flat M(QE)4 spacetime satisfying Einstein field\nequation without cosmological constant. Finally we give a nontrivial example of\na M(QE)4 spacetime to establish the existence of it.\n