Harmonic Sections of Tangent Bundles with Horizontal Sasaki Gradient Metric

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

References

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