Some notes on vector fields in the tangent bundle

Let (M,g)be a Riemannian manifold and T (M) its tangent bundle with the horizontal lift H∇ of the affine connection ∇ of M. The aims of the present paper are to study conditions of infinitesimal affine transformation for vertical and horizontal vector fields in the tangent bundle and to give necessa...

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Bibliographic Details
Published in:New trends in mathematical sciences 2019-12, Vol.4 (7), p.465-472
Main Authors: Cengiz, Nejmi, Yildirim, Furkan, Akbulut, Kürsat
Format: Article
Language:English
Subjects:
Affine transformations
Fields (mathematics)
Riemann manifold
Online Access:Get full text
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Summary:Let (M,g)be a Riemannian manifold and T (M) its tangent bundle with the horizontal lift H∇ of the affine connection ∇ of M. The aims of the present paper are to study conditions of infinitesimal affine transformation for vertical and horizontal vector fields in the tangent bundle and to give necessary conditions for vertical, complete and horizontal vector fields in the tangent bundle to be a harmonic vector fields with respect to the horizontal lift H∇ of the affine connection ∇ of M.Keywords: Lift, Riemannian manifold, tangent bundle, infinitesimal Affine transformation, harmonic vector field.
ISSN:2147-5520
2147-5520
DOI:10.20852/ntmsci.2019.387