8 Results Found

We introduce a special vector field $\omega$ on a Riemannian manifold $(N^m,g)$, such that the Lie derivative of the metric g with respect to $\omega$ is equal to $\rho Ric$, where $Ric$ is the Ricci tensor of $(N^m,g)$ and $\rho$ is a smooth function on $N^m$. We c...

For a compact Riemannian m-manifold $(M^m,g),m>1,$ endowed with a nontrivial conformal vector field $\zeta$ with a conformal factor $\sigma$, there is an associated skew-symmetric tensor $\phi$ called the associated tensor, and also, $\zeta$ admits the H...

The target of the current research article is to investigate the solitonic attributes of relativistic magneto-fluid spacetime (MFST) if its metrics are Ricci–Yamabe soliton (RY-soliton) and gradient Ricci–Yamabe soliton (GRY-soliton). We...

We extend the study of orientable hypersurfaces in a Sasakian manifold initiated by Watanabe. The Reeb vector field $\xi$ of the Sasakian manifold induces a vector field ${\xi }^T$ on the hypersurface, namely the tangential component of $\&$...

Minimal compact hypersurface in the unit sphere ${\mathbb{S}}^{n+1}$ having squared length of shape operator ${∥A∥}^2<n$ are totally geodesic and with ${∥A∥}^2=n$ are Clifford hypersurfaces. Therefore, classifying totally geodesic hypersurfaces and Clifford hypersurfaces has i...

A two-fluid model can be described by an anisotropic fluid matter, and we introduced the notion of an anisotropic fluid spacetime. The algebraic and differential properties of an anisotropic fluid spacetime equipped with several forms of the stress&n...

$f(\mathcal{R},T)$-gravity is a generalization of Einstein’s field equations $\left({EFE}_s\right)$ and $f\left(\mathcal{R}\right)$-gravity. In this research article, we demonstrate the virtues of the $f(\mathcal{R},T)$-gravity model with Einstein solitons $\left(ES\right)$ and gradient Einstein solitons $\left(GES\right)$. We acqu...

We investigate left-invariant generalized cross-curvature solitons on simply connected three-dimensional Lorentzian Lie groups. Working with the assumption that the contravariant tensor $P_{ij}$ (defined from the Ricci tensor and scalar curvature) is inve...