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On the geometry of the tangent bundle with gradient Sasaki metric
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PurposeLet (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/approachIn this paper the authors introduce a new class of natural metrics called gradient Sasaki metric on tangent bundle.FindingsThe 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/valueThe 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.
Title: On the geometry of the tangent bundle with gradient Sasaki metric
Description:
PurposeLet (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/approachIn this paper the authors introduce a new class of natural metrics called gradient Sasaki metric on tangent bundle.
FindingsThe 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/valueThe 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.
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