- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 68 Issue: 1
- On the Geometry of the Tangent Bundle With Vertical Rescaled Metric
On the Geometry of the Tangent Bundle With Vertical Rescaled Metric
Authors : Hamou Mohammed Dida, Fouzi Hathout, Abdelhalim Azzouz
Pages : 222-235
Doi:10.31801/cfsuasmas.443735
View : 5 | Download : 4
Publication Date : 2019-02-01
Article Type : Research
Abstract :Let (M,g) be a n-dimensional smooth Riemannian manifold. In the present paper, we introduce a new class of natural metrics denoted by G^{f} and called the vertical rescaled metric on the tangent bundle TM. We calculate its Levi-Civita connection and Riemannian curvature tensor. We study the geometry of (TM,G^{f}) and several important results are obtained on curvature, Einstein structure, scalar and sectional curvaturesKeywords : Tangent bundle, vertical rescaled metric, Einstein structure, curvature