Projective Vector Fields on Semi-Riemannian Manifolds

Norah Alshehri () and Mohammed Guediri
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Norah Alshehri: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Mohammed Guediri: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2024, vol. 12, issue 18, 1-12

Abstract: This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field P on such a manifold is also a conformal vector field with potential function ψ and the vector field ζ dual to d ψ does not change its causal character, then P is homothetic, or ζ is a light-like vector field. Additionally, it is shown that a complete Riemannian manifold admits a projective vector field that is also conformal and non-Killing if and only if it is locally Euclidean. The paper also presents other results related to the characterization of Killing and parallel vector fields using the Ricci curvature and the Hessian of the function given by the inner product of the vector field.

Keywords: semi-Riemannian manifolds; projective vector fields; conformal and Killing vector fields; Ricci curvature; Hessian (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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