Berger Type Deformed Sasaki Metric and Harmonicity on the Cotangent Bundle

Abstract

In this paper, we introduce the Berger type deformed Sasaki metric on the cotangent bundle $T^{\ast}M$ over an anti-paraKähler manifold $(M, \varphi, g)$. We establish a necessary and sufficient conditions under which a covector field is harmonic with respect to the Berger type deformed Sasaki metric. We also construct some examples of harmonic vector fields. we also study the harmonicity of a map between a Riemannian manifold and a cotangent bundle of another Riemannian manifold and vice versa.

Keywords

• Cotangent bundles
• horizontal lift and vertical lift
• Berger type deformed Sasaki metric
• harmonic maps

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