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Publication date: 3 May 2021

Lakehal Belarbi and Hichem Elhendi

Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient…

Abstract

Purpose

Let (M, g) be a n-dimensional smooth Riemannian manifold. In the present paper, the authors introduce a new class of natural metrics denoted by gf and called gradient Sasaki metric on the tangent bundle TM. The authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM, gf) and several important results are obtained on curvature, scalar and sectional curvatures.

Design/methodology/approach

In this paper the authors introduce a new class of natural metrics called gradient Sasaki metric on tangent bundle.

Findings

The authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM,gf) and several important results are obtained on curvature scalar and sectional curvatures.

Originality/value

The authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of (TM,gf) and several important results are obtained on curvature scalar and sectional curvatures.

Details

Arab Journal of Mathematical Sciences, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1319-5166

Keywords

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