A study of harmonicity on cotangent bundle with Berger-type deformed Sasaki metric over standard K\"{a}hler manifold
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In this paper, we present some results concerning the harmonicity on the cotangent bundle equipped with the Berger-type deformed Sasaki metric over standard K\"{a}hler manifolds. We establish necessary and sufficient conditions under which a covector field is harmonic map or is harmonic covector with respect to the Berger-type deformed Sasaki metric and we construct some examples of harmonic covector fields. We also study the harmonicity of a covector field along a map between Riemannian manifolds, the target manifold being standard K\"{a}hler equipped with the Berger-type deformed Sasaki metric on its cotangent bundle. After that, we discuss the harmonicity of the composition of the projection map of the cotangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold, the source manifold being standard K\"{a}hler whose cotangent bundle is endowed with the Berger-type deformed Sasaki metric.
Abstract
In this paper, we present some results concerning the harmonicity on the cotangent bundle equipped with the Berger-type deformed Sasaki metric over standard K\"{a}hler manifolds. We establish necessary and sufficient conditions under which a covector field is harmonic map or is harmonic covector with respect to the Berger-type deformed Sasaki metric and we construct some examples of harmonic covector fields. We also study the harmonicity of a covector field along a map between Riemannian manifolds, the target manifold being standard K\"{a}hler equipped with the Berger-type deformed Sasaki metric on its cotangent bundle. After that, we discuss the harmonicity of the composition of the projection map of the cotangent bundle of a Riemannian manifold with a map from this manifold into another Riemannian manifold, the source manifold being standard K\"{a}hler whose cotangent bundle is endowed with the Berger-type deformed Sasaki metric.
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