Work

Projective Vector Fields on Semi-Riemannian Manifolds

Year: 2024

Type: article

Abstract: This paper explores the properties of projective vector fields on semi-Riemannian manifolds. The main result establishes that if a projective vector field η on such a manifold is also a conformal vector field with potential function ψ, then η must either be homothetic, or the vector field ζ, which is dual to dψ, 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.

Source: Mathematics

DOI: 10.3390/math12182914

Authors: Norah Alshehri, Mohammed Guediri

Institution: King Saud University

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: King Saud University