Ricci Solitons on Riemannian Hypersurfaces Generated by Torse-Forming Vector Fields in Riemannian and Lorentzian Manifolds
axioms
In this paper, we examine torse-forming vector fields to characterize extrinsic
spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in
Riemannian and Lorentzian manifolds. First, we analyze the properties of these vector fields
on Riemannian manifolds. Next, we focus on Ricci solitons on Riemannian hypersurfaces
induced by torse-forming vector fields of Riemannian or Lorentzian manifolds. Specifically,
we show that such a hypersurface in the manifold with constant sectional curvature is
either totally geodesic or an extrinsic sphere.
In this paper, we examine torse-forming vector fields to characterize extrinsic
spheres (that is, totally umbilical hypersurfaces with nonzero constant mean curvatures) in
Riemannian and…
We study the characteristics of affine vector fields on pseudo-Riemannian manifolds and provide tensorial formulas that characterize these vector fields. Using our approach, we present a…
Considering an almost Ricci soliton (ARS) (N, g, iii, kappa) on a compact Riemannian manifold (N, g), we use the Ricci curvature in the direction of the potential vector field iii to derive…