Killing and 2-Killing Vector Fields on Doubly Warped Products

Adara M. Blaga () and Cihan Özgür
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Adara M. Blaga: Department of Mathematics, West University of Timişoara, 300223 Timişoara, Romania
Cihan Özgür: Department of Mathematics, İzmir Democracy University, İzmir 35140, Türkiye

Mathematics, 2023, vol. 11, issue 24, 1-14

Abstract: We provide a condition for a 2-Killing vector field on a compact Riemannian manifold to be Killing and apply the result to doubly warped product manifolds. We establish a connection between the property of a vector field on a doubly warped product manifold and its components on the factor manifolds to be Killing or 2-Killing. We also prove that a Killing vector field on the doubly warped product gives rise to a Ricci soliton factor manifold if and only if it is an Einstein manifold. If a component of a Killing vector field on the doubly warped product is of a gradient type, then, under certain conditions, the corresponding factor manifold is isometric to the Euclidean space. Moreover, we provide necessary and sufficient conditions for a doubly warped product to reduce to a direct product. As applications, we characterize the 2-Killing vector fields on the doubly warped spacetimes, particularly on the standard static spacetime and on the generalized Robertson–Walker spacetime.

Keywords: 2-Killing vector field; doubly warped product manifold; spacetime; Ricci soliton (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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