Search

Showing total 3 results
3 results

1. On 4-dimensional almost para-complex pure-Walker manifolds

Author

Sibel Turanli, Hilmi Sarsilmaz, and Murat Iscan

Subjects
Pure mathematics, General Mathematics, Injective metric space, Mathematical analysis, Structure (category theory), Fubini–Study metric, Mathematics::Geometric Topology, Manifold, Almost para-complex structure,pure metric,neutral metric,Walker metric,Kähler structure, Metric (mathematics), Mathematics::Differential Geometry, Mathematics::Symplectic Geometry, Fisher information metric, Mathematics
Abstract

This paper is concerned with almost para-complex structures on Walker 4-manifolds. For these structures, we study some problems of Kahler manifolds. We also give an example of a flat almost para-complex manifold, which consists of a nonintegrable almost para-complex structure on Walker 4-manifolds.

Published
2015

2. 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

3. Semi-slant and bi-slant submanifolds of almost contact metric 3-structure manifolds

Author

Fereshteh Malek and Mohammad Bagher Kazemi Balgeshir

Subjects
Pure mathematics, Almost contact 3-structure manifold,semi-slant and bi-slant submanifold,3-Sasakian manifold, General Mathematics, Computer Science::Computer Vision and Pattern Recognition, Mathematical analysis, Mathematics::History and Overview, Physics::Optics, Mathematics::Differential Geometry, Invariant (mathematics), Mathematics::Symplectic Geometry, Manifold, Computer Science::Computers and Society, Mathematics
Abstract

In this paper we introduce the notions of semi-slant and bi-slant submanifolds of an almost contact 3-structure manifold. We give some examples and characterization theorems about these submanifolds. Moreover, the distributions of semi-slant submanifolds of 3-cosymplectic and 3-Sasakian manifolds are studied. ϕi)i=1;2;3 and the vector elds should be slant or invariant with respect to all of the ϕi's. Therefore, it is a generalization of invariant, anti-invariant, slant, semi-slant, and bi-slant submanifolds in almost contact metric 3-structures and we denote them by 3- semi-slant and 3-bi-slant submanifolds. Following the approaches of (3, 13), we characterized 3-bi-slant and 3-semi-slant submanifolds and studied geometric properties of distributions of these submanifolds where the ambient manifolds are 3-Sasakian or 3-cosymplectic. It should be noted that, in the denition of semi-slant

Published
2014