M-Projective Curvature Tensor and Ricci-Bourguignon Soliton on Lorentzian β-Kenmotsu Manifold

Abstract

The prime object of the present article is to explore the characteristics of a Lorentzian β-K enmotsu manifold (M_β) admitting an M-projective curvature tensor. We derived characteristic theorems for M_β satisfying M-projectively ϕ-recurrent and pseudo-symmetric conditions. ϕ −M-projectively flat M_β is the subject of our next analysis. Additionally, we deal with the M_β satisfying M-projectively Ricci pseudo-symmetric condition. Next, we describe the M_β satisfying R(ζ,B₃) · M = 0 condition.
Further, we discuss cyclic parallel Ricci tensor, V ^♭-parallel Ricci tensor and Ricci-Bourguignon soliton in M_β. Finally, we have presented an example of an M_β.

Keywords: Lorentzian β-Kenmotsu manifold (M_β), M-projective curvature tensor, generalized V ^♭-Einstein manifold, Ricci pseudo symmetric, and Ricci-Bourguignon soliton (RBS).

2010 Mathematics Subject Classification. 53C05; 53C15; 53C20; 53C25; 53D15; 53D10