On the Geometry of the Tangent Bundle With Vertical Rescaled Metric

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume: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 DİDA, Fouzi HATHOUT, Abdelhalim AZZOUZ

Pages : 222-235

Doi:10.31801/cfsuasmas.443735

View : 38 | Download : 12

Publication Date : 2019-02-01

Article Type : Research Paper

Abstract :Let insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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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