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1. Notes on the tangent bundle with deformed complete lift metric

Author

Mustafa Özkan and Aydin Gezer

Subjects
Tangent bundle, General Mathematics, Mathematical analysis, Geometry, Levi-Civita connection, Tensor field, symbols.namesake, Mathematics::Algebraic Geometry, Unit tangent bundle, Almost complex structure,holomorphic tensor field,Kähler-Norden metric,Killing vector field,Riemannian curvature tensors, symbols, Hermitian manifold, Curvature form, Mathematics::Differential Geometry, Exponential map (Riemannian geometry), Metric connection, Mathematics
Abstract

In this paper, our aim is to study some properties of the tangent bundle with a deformed complete lift metric.

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. Foliations and a class of metrics on tangent bundle

Author

Leila Nourmohammadi Far and Esmaeil Peyghan

Subjects
Tangent bundle, Pure mathematics, General Mathematics, Mathematical analysis, Levi-Civita connection, symbols.namesake, Hyperbolic set, Unit tangent bundle, symbols, Finsler manifold,foliation,constant curvature,Riemannian metric, Hermitian manifold, Mathematics::Metric Geometry, Sectional curvature, Finsler manifold, Mathematics::Differential Geometry, Exponential map (Riemannian geometry), Mathematics::Symplectic Geometry, Mathematics
Abstract

Let M be a smooth manifold with Finsler metric F, and let TM° be the slit tangent bundle of M with a generalized Riemannian metric G, which is induced by F. In this paper, we extract many natural foliations of (TM°,G) and study some of their geometric properties. Next we use this approach to obtain new characterizations of Finsler manifolds with positive constant curvature.

Published
2014