Unit tangent sphere bundles with the Kaluza-Klein metric satisfying some commutative conditions

2024-11-20T07:59:08+00:00

Let $(M,g)$ be an $n-$dimensional Riemannian manifold and $T_{1}M$ its tangent sphere bundle with the contact metric structure $(\tilde{G},\eta ,\phi ,\xi )$, where $\tilde{G}$ is the Kaluza-Klein metric. Let $\tilde{S}$ be the Ricci operator and $h$ be the structural operator on $T_{1}M$. In this paper, we find some conditions for the relations $\tilde{S}h=h\tilde{S}$ and $\tilde{S}\phi h=\phi h\tilde{S}$ to be satisfied.

Riemannian CR manifolds and ρ-Einstein solitons: a geometric analysis and applications

2024-12-03T08:58:03+00:00

In this article, we investigate $\rho$-Einstein solitons on Riemannian CR manifolds. Specifically, we explore the properties of $\rho$-Einstein solitons in the presence of cyclic $\eta$-recurrent Ricci tensors on Riemannian CR manifolds. We also examine these solitons with respect to Torse-forming vector fields. Additionally, we study $\rho$-Einstein solitons satisfying Ricci semi-symmetric condition on Riemannian CR manifolds. Furthermore, we examine the properties of conharmonic and conformal curvature tensors on Riemannian CR manifolds admitting $\rho$-Einstein solitons. Finally, we discuss the applications of $\rho$-Einstein solitons and their potential uses in various fields.

International Journal of Maps in Mathematics

Unit tangent sphere bundles with the Kaluza-Klein metric satisfying some commutative conditions

Riemannian CR manifolds and ρ-Einstein solitons: a geometric analysis and applications