Affiliation:
1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia
2. 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 (fB×bF,Π=μvΠBh+νhΠFv,g) and express the Levi-Civita contravariant connection, curvature and metacurvature of (fB×bF,Π,g) in terms of Levi-Civita connections, curvatures and metacurvatures of components (B,ΠB,gB) and (F,ΠF,gF). We also study compatibility conditions related to the Poisson structure Π and the contravariant metric g on fB×bF, so that the compatibility conditions on (B,ΠB,gB) and (F,ΠF,gF) remain consistent in the Poisson doubly warped product manifold (fB×bF,Π,g).
Funder
Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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