On mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons

2025/03/14 by Yan, Junhao, Bi, Ran, Lu, Weijun
#53C15 #53C25 #53C35 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.11296

Abstract

This paper delves into the study of mixed super quasi-Einstein manifolds of dimension n (for short, \rm Mⁿ_SQE), focusing on their geometric and physical attributes. Initially, we explore several properties of \rm Mⁿ_SQE, including conformal Ricci pseudosymmetry, Einstein's field equation, and the space-matter tensor. Subsequently, we characterize mixed super quasi-Einstein manifolds that admit Ricci-Bourguignon solitons. We establish that if the generator vector field is torse-forming, the manifold reduces to a pseudo generalized quasi-Einstein manifold, and we provide a detailed characterization of the eigenvalue problem associated with the symmetric tensor. To substantiate our findings, we construct an example to illustrate the existence of mixed super quasi-Einstein spacetime.

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