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Killing and 2-Killing 1-Forms on Poisson Doubly Warped Product Manifolds

Author

Listed:
  • Bang-Yen Chen

    (Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA)

  • Majid Ali Choudhary

    (Department of Mathematics, Maulana Azad National Urdu University, Hyderabad 500032, India)

  • Foued Aloui

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia)

  • Ibrahim Al-Dayel

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 65892, Riyadh 11566, Saudi Arabia)

Abstract

In this paper we investigate Killing and 2-Killing 1-forms on a Poisson doubly warped product manifold ( PDWPM ). We establish a connection between the property of 1-form on a PDWPM and its components on the factor manifolds to be Killing or 2-Killing. We also demonstrate that a Killing 1-form on a PDWPM generates a contravariant Ricci soliton factor manifold if and only if it is a contravariant Einstein manifold. Additionally, we provide necessary and sufficient conditions for a PDWPM to be a Poisson singly warped product manifold ( PSWPM ). Finally, we present examples of Killing and 2-Killing 1-forms on PDWPM s with one-dimensional, and two-dimensional base spaces.

Suggested Citation

  • Bang-Yen Chen & Majid Ali Choudhary & Foued Aloui & Ibrahim Al-Dayel, 2026. "Killing and 2-Killing 1-Forms on Poisson Doubly Warped Product Manifolds," Mathematics, MDPI, vol. 14(2), pages 1-25, January.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:2:p:301-:d:1840752
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