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Poisson Doubly Warped Product Manifolds

Author

Listed:
  • Ibrahim Al-Dayel

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

  • Foued Aloui

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

  • Sharief Deshmukh

    (Department of Mathematics, King Saud University, Riyadh 11495, Saudi Arabia)

Abstract

This article generalizes some geometric structures on warped product manifolds equipped with a Poisson structure to doubly warped products of pseudo-Riemannian manifolds equipped with a doubly warped Poisson structure. First, we introduce the notion of Poisson doubly warped product manifold ( f B × b F , Π = μ v Π B h + ν h Π F v , g ) and express the Levi-Civita contravariant connection, curvature and metacurvature of ( f B × b F , Π , g ) in terms of Levi-Civita connections, curvatures and metacurvatures of components ( B , Π B , g B ) and ( F , Π F , g F ) . We also study compatibility conditions related to the Poisson structure Π and the contravariant metric g on f B × b F , so that the compatibility conditions on ( B , Π B , g B ) and ( F , Π F , g F ) remain consistent in the Poisson doubly warped product manifold ( f B × b F , Π , g ) .

Suggested Citation

  • Ibrahim Al-Dayel & Foued Aloui & Sharief Deshmukh, 2023. "Poisson Doubly Warped Product Manifolds," Mathematics, MDPI, vol. 11(3), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:519-:d:1039867
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