Characterizing Affine Vector Fields on Pseudo-Riemannian Manifolds

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. Mo...

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Bibliographic Details
Main Authors: Norah Alshehri, Mohammed Guediri
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Axioms
Subjects:
affine, killing, and parallel vector fields
geodesic vector fields
Laplacian
Hessian
Bochner formula
Online Access:https://www.mdpi.com/2075-1680/13/12/835
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Summary: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.
ISSN:2075-1680

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