Journal of the
Korean Mathematical Society JKMS

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. 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 Riemannina manifold with a map from this manifold into another Riemannian manifold.

Keywords: Anti-paraK\"{a}hler manifold, tangent bundle, Berger-type Cheeger-Gromoll metric, harmonic maps

MSC numbers: 53C43, 58E20, 53C15, 53C07