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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. 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