Harmonic Sections of Tangent Bundles with Horizontal Sasaki Gradient Metric

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Hagia Sophia Journal of Geometry
Volume:3 Issue:2
Harmonic Sections of Tangent Bundles with Horizontal Sasaki Gradient Metric

Harmonic Sections of Tangent Bundles with Horizontal Sasaki Gradient Metric

Authors : Abderrahım ZAGANE

Pages : 31-40

View : 40 | Download : 10

Publication Date : 2021-12-27

Article Type : Research Paper

Abstract :In this paper, we introduce harmonic sections of tangent bundles with horizontal Sasaki gradient metric, then we establish necessary and sufficient conditions under which a vector field is harmonic with respect to this metric. We also construct some examples of harmonic vector fields. After that, we study the harmonicity of the maps between a Riemannian manifold and the tangent bundle over another Riemannian manifold or vice versa.
Keywords : tangent bundles, horizontal Sasaki gradient metric, harmonic maps

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