Contravariant Curvatures of Doubly Warped Product Poisson Manifolds

Foued Aloui (), Shyamal Kumar Hui and Ibrahim Al-Dayel
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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
Shyamal Kumar Hui: Department of Mathematics, The University of Burdwan, Golapbag, Burdwan 713104, West Bengal, India
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

Mathematics, 2024, vol. 12, issue 8, 1-20

Abstract: In this paper, we investigate the sectional contravariant curvature of a doubly warped product manifold ( f B × b F , g ˜ , Π = Π B + Π F ) equipped with a product Poisson structure Π , using warping functions and sectional curvatures of its factor manifolds ( B , g ˜ B , Π B ) and ( F , g ˜ F , Π F ) . Qualar and null sectional contravariant curvatures of ( f B × b F , g ˜ , Π ) are also given. As an example, we construct a four-dimensional Lorentzian doubly warped product Poisson manifold where qualar and sectional curvatures are obtained.

Keywords: doubly warped product; Poisson geometry; sectional contravariant curvature; qualar; curvature (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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