Covector Fields which are Harmonic Maps in the Cotangent Bundle Equipped with the Horizontally Deformed Sasaki Metric

In this paper, we investigate some harmonicity properties of a covector field in the cotangent bundle endowed with the horizontally deformed Sasaki metric, and then we establish necessary and sufficient conditions for a covector field to be a harmonic map (or harmonic covector field) concerning this metric. We also provide explicit examples of such harmonic covector fields to illustrate the theoretical results.