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1 – 1 of 1Lakehal 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 Sasaki…
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
Originality/value
The authors calculate its Levi-Civita connection and Riemannian curvature tensor. The authors study the geometry of
Details