In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds. We show that this is obtained if the total space is an b-almost Kenmotsu manifold. | Turkish Journal of Mathematics Research Article Turk J Math (2014) 38: 778 – 788 ¨ ITAK ˙ c TUB ⃝ doi: Almost contact metric submersions and symplectic manifolds Augustin BATUBENGE1,∗, Tshikunguila TSHIKUNA-MATAMBA2 Department of Mathematical Sciences, College of Science, Engineering, and Technology, University of South Africa, Unisa, Pretoria, South Africa 2 Department of Mathematics, Institut Sup´erieur P´edagogique, Kananga, Democratic Republic of the Congo 1 Received: • Accepted: • Published Online: • Printed: Abstract: In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds. We show that this is obtained if the total space is an b-almost Kenmotsu manifold. Key words: Riemannian submersions, almost Hermitian manifolds, almost contact metric manifolds, almost contact metric submersions, symplectic manifolds 1. Introduction The theory of almost contact submersions intertwines contact geometry with the almost Hermitian one. For instance, the fibers of an almost contact metric submersion of type I, in the sense of Watson [12], are almost Hermitian manifolds. However, certain classes of almost Hermitian manifolds are closely related to symplectic manifolds. Specifically, almost K¨ahler manifolds are endowed with symplectic structure while quasi-K¨ahlerian manifolds are related to (1, 2)-symplectic ones. Almost contact metric and almost symplectic manifolds were developed in [1], but in [4], the concept of k -symplectic manifolds was extensively studied. In this paper, we study almost contact metric submersions involving symplectic structures. It is organized in the following way. In Section 2, devoted to the preliminaries on manifolds, we review the main classes of almost Hermitian manifolds that have some relation with almost symplectic structures; almost contact metric manifolds that can be
