1. Horizontally submersions of contact CR-submanifolds
- Author
-
Tshikunguila Tshikuna-Matamba and Fortuné Massamba
- Subjects
Riemannian submersion ,General Mathematics ,Mathematical analysis ,Tangent ,Curvature ,Manifold ,CR-submanifold,almost Hermitian manifold,almost contact metric submersion,symplectic manifold,horizontal submersion ,symbols.namesake ,symbols ,Hermitian manifold ,Mathematics::Differential Geometry ,Complex manifold ,Mathematics::Symplectic Geometry ,Symplectic geometry ,Symplectic manifold ,Mathematics - Abstract
In this paper, we discuss some geometric properties of almost contact metric submersions involving symplectic manifolds. We show that the structures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds are related to (1, 2)-symplectic structures. For horizontally submersions of contact CR-submanifolds of quasi-K-cosymplectic and quasi-Kenmotsu manifolds, we study the principal characteristics and prove that their total spaces are CR-product. Curvature properties between curvatures of quasi-K-cosymplectic and quasi-Kenmotsu manifolds and the base spaces of such submersions are also established. We finally prove that, under a certain condition, the contact CR-submanifold of a quasi Kenmotsu manifold is locally a product of a totally geodesic leaf of an integrable horizontal distribution and a curve tangent to the normal distribution.
- Published
- 2014