On the Geometry of the Tangent Bundle With Vertical Rescaled Metric

Year 2019, Volume: 68 Issue: 1, 222 - 235, 01.02.2019

Hamou Mohammed Dida Fouzi Hathout , Abdelhalim Azzouz

https://doi.org/10.31801/cfsuasmas.443735

Cited By: 4

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 curvatures

Keywords

Tangent bundle, vertical rescaled metric, Einstein structure, curvature

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