7 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...

$f(\mathcal{R},T)$-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...