Year: 2024
Type: article
Abstract: 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.
Source: Axioms
Authors: Norah Alshehri, Mohammed Guediri
Institution: King Saud University
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
Funder: King Saud University
Award: G440015274
OpenAlex ID: W4404821400