Contravariant Curvatures of Doubly Warped Product Poisson Manifolds
Foued Aloui,
Shyamal Kumar Hui,
Ibrahim Al-Dayel
Affiliations
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
In this paper, we investigate the sectional contravariant curvature of a doubly warped product manifold ( fB×bF,g˜,Π=ΠB+ΠF) equipped with a product Poisson structure Π, using warping functions and sectional curvatures of its factor manifolds (B,g˜B,ΠB) and (F,g˜F,ΠF). Qualar and null sectional contravariant curvatures of ( fB×bF,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.
