Ricci Solitons on Riemannian Hypersurfaces Generated by Torse-Forming Vector Fields in Riemannian and Lorentzian Manifolds
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.
An odd-dimensional sphere admits a killing vector field, induced by the transform of the unit normal by the complex structure of the ambiant Euclidean space. In this paper, we studied orientable…
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…
This paper investigates compact Riemannian hypersurfaces immersed in (n+1)-dimensional Riemannian or Lorentzian manifolds that admit concircular vector fields, also known as closed conformal…