Study of some harmonicity problems concerning the rescaled Sasaki metric

Abstract

This paper introduces the concept of harmonicity on the tangent bundle endowed with a rescaled Sasaki metric. Firstly, we study the harmonicity of a vector field on the tangent bundle. Secondly, we investigate the harmonicity of the composition of a vector field and mapping between Riemannian manifolds. Afterwards, we explore the harmonicity of composition between the natural projection of a Riemannian manifold and a map of this manifold to another. Finally, we investigate the harmonicity of the tangent map.