Characterizing Affine Vector Fields on Pseudo-Riemannian Manifolds
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 straightforward proof that any affine vector field on a compact Riemannian manifold is a Killing vector field. Moreover, we establish several necessary and sufficient conditions for an affine vector field on a Riemannian manifold to be classified as a Killing or parallel vector field.
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…
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…