Đang chuẩn bị liên kết để tải về tài liệu:
Horizontally submersions of contact CR-submanifolds

Không đóng trình duyệt đến khi xuất hiện nút TẢI XUỐNG Tải xuống

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 quasiKenmotsu manifolds, we study the principal characteristics and prove that their total spaces are CR-product. | Turkish Journal of Mathematics http://journals.tubitak.gov.tr/math/ Research Article Turk J Math (2014) 38: 436 – 453 ¨ ITAK ˙ c TUB ⃝ doi:10.3906/mat-1303-44 Horizontally submersions of contact CR-submanifolds 1 Fortun´ e MASSAMBA1,∗, Tshikunguila TSHIKUNA-MATAMBA2 School of Mathematics, Statistics, and Computer Science, University of KwaZulu-Natal, Scottsville, South Africa 2 Department of Mathematical Sciences, College of Science, Engineering, and Technology, University of South Africa, Pretoria, South Africa Received: 22.03.2013 • Accepted: 09.08.2013 • Published Online: 14.03.2014 • Printed: 11.04.2014 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 quasiKenmotsu 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. Key words: CR -submanifold, almost Hermitian manifold, almost contact metric submersion, symplectic manifold, horizontal submersion 1. Introduction Riemannian submersions between Riemannian manifolds were initiated by O’Neill [14]. Almost contact metric submersions were developed by Chinea [8] and Watson [17]. The theory of almost contact metric submersions intertwines contact geometry with the almost Hermitian one. For instance, the base space of an almost contact metric submersion of type II , in the