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Killing and 2-Killing Vector Fields on Doubly Warped Products

Author

Listed:
  • Adara M. Blaga

    (Department of Mathematics, West University of Timişoara, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

  • Cihan Özgür

    (Department of Mathematics, İzmir Democracy University, İzmir 35140, Türkiye
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Adara M. Blaga & Cihan Özgür, 2023. "Killing and 2-Killing Vector Fields on Doubly Warped Products," Mathematics, MDPI, vol. 11(24), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4983-:d:1301854
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    References listed on IDEAS

    as
    1. H. K. El-Sayied & Sameh Shenawy & Noha Syied, 2016. "Conformal Vector Fields on Doubly Warped Product Manifolds and Applications," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-11, October.
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