Search Results (4)

This paper undertakes a detailed study of $\eta$-Ricci–Bourguignon solitons on $ϵ$-Kenmotsu manifolds, with particular focus on three special types of Ricci tensors: Codazzi-type, cyclic parallel and cyclic $\eta$-recurrent tensors that support such solitonic structures. We derive key curvature conditions satisfying Ricci semi-symmetric $(R·E=0)$, conharmonically Ricci semi-symmetric $(C(\xi ,{\beta }_X)·E=0)$, $\xi$-projectively flat $(P({\beta }_X,{\beta }_Y)\xi =0)$, projectively Ricci semi-symmetric $(L·P=0)$ and $W_5$-Ricci semi-symmetric $(W(\xi ,{\beta }_Y)·E=0)$, respectively, with the admittance of $\eta$-Ricci–Bourguignon solitons. This work further explores the role of torse-forming vector fields and provides a thorough characterization of $\varphi$-Ricci symmetric indefinite Kenmotsu manifolds admitting $\eta$-Ricci–Bourguignon solitons. Through in-depth analysis, we establish significant geometric constraints that govern the behavior of these manifolds. Finally, we construct explicit examples of indefinite Kenmotsu manifolds that satisfy the $\eta$-Ricci–Bourguignon solitons equation, thereby confirming their existence and highlighting their unique geometric properties. Moreover, these solitonic structures extend soliton theory to indefinite and physically meaningful settings, enhance the classification and structure of complex geometric manifolds by revealing how contact structures behave under advanced geometric flows and link the pure mathematical geometry to applied fields like general relativity. Furthermore, $\eta$-Ricci–Bourguignon solitons provide a unified framework that deepens our understanding of geometric evolution and structure-preserving transformations. Full article

This paper concerns certain properties of projective curvature tensor, conharmonic curvature tensor, quasi-conharmonic curvature tensor, and Ricci semi-symmetric conditions with respect to the general connection in an LP-Sasakian manifold. We also provide the applications of LP-Sasakian manifolds admitting general connections in the context of the general theory of relativity. Full article

The main aim of the proposed paper is to investigate the lifts of Kenmotsu manifolds that admit NSNMC in the tangent bundle. We investigate several properties of the lifts of the curvature tensor, the conformal curvature tensor, and the conharmonic curvature tensor of Kenmotsu manifolds that admit NSNMC in the tangent bundle. We also study and discover that the lift of the Kenmotsu manifold that admit NSNMC is regular in the tangent bundle. Additionally, we find that the data provided by the lift of Ricci soliton on the lift of Ricci semi-symmetric Kenmotsu manifold that admits NSNMC in the tangent bundle are expanding. Full article

The motive of the current article is to study and characterize the geometrical and physical competency of the conharmonic curvature inheritance (Conh CI) symmetry in spacetime. We have established the condition for its relationship with both conformal motion and conharmonic motion in general and Einstein spacetime. From the investigation of the kinematical and dynamical properties of the conformal Killing vector (CKV) with the Conh CI vector admitted by spacetime, it is found that they are quite physically applicable in the theory of general relativity. We obtain results on the symmetry inheritance for physical quantities ($\mu ,p,u_i,{\sigma }_{ij},\eta ,q_i$) of the stress-energy tensor in imperfect fluid, perfect fluid and anisotropic fluid spacetimes. Finally, we prove that the conharmonic curvature tensor of a perfect fluid spacetime will be divergence-free when a Conh CI vector is also a CKV. Full article