Poisson Doubly Warped Product Manifolds

Ibrahim Al-Dayel (), Foued Aloui and Sharief Deshmukh
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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

Mathematics, 2023, vol. 11, issue 3, 1-14

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 ) .

Keywords: doubly warped product; Poisson geometry; Levi-Civita contravariant connection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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