Harmonic Sections of Tangent Bundles with Horizontal Sasaki Gradient Metric

Year 2021, Volume: 3 Issue: 2, 31 - 40, 27.12.2021

Abderrahım Zagane

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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