A study of harmonicity on tangent bundles with the Berger-type Cheeger-Gromoll metric
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This paper aims to study the harmonicity concerning the Berger-type Cheeger-Gromoll metric on the tangent bundle over an anti-paraK\"{a}hler manifold. Firstly, the harmonicity of a vector field is studied for this metric, and some examples of harmonic vector fields are given. Secondly, the harmonicity of a vector field along a mapping between Riemannian manifolds has been discussed. The last section of this paper examines the harmonicity of the composition of the projection map of the tangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold.
Abstract
This paper aims to study the harmonicity concerning the Berger-type Cheeger-Gromoll metric on the tangent bundle over an anti-paraK\"{a}hler manifold. Firstly, the harmonicity of a vector field is studied for this metric, and some examples of harmonic vector fields are given. Secondly, the harmonicity of a vector field along a mapping between Riemannian manifolds has been discussed. The last section of this paper examines the harmonicity of the composition of the projection map of the tangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold.