$2-$Killing Vector Fields on Warped Product Manifolds

TL;DR

This paper investigates 2-Killing vector fields on warped product manifolds, characterizing their properties on specific space-times, and explores their relation to curvature and parallelism in these geometric structures.

Contribution

It provides new characterizations of 2-Killing vector fields on warped products and applies these results to well-known space-time models.

Findings

Conditions for 2-Killing vector fields to be parallel

Relations between 2-Killing vector fields and curvature

Descriptions of 2-Killing vector fields in specific space-time models

Abstract

The present article provides a study of $2-$Killing vector fields on warped product manifolds as well as characterization of this structure on standard static and generalized Robertson-Walker space-times. Some conditions for a $2-$Killing vector field on a warped product manifold to be parallel are obtained. Moreover, some results on the curvature of a warped product manifolds in terms of $2-$Killing vector fields are derived. Finally, we apply our results to describe $2-$Killing vector fields of some well known warped product space-time models.