Vertical rescaled Cheeger-Gromoll metric and harmonicity on the cotangent bundleA. Zagane, A. GezerIn this paper, we introduce the harmonicity on the cotangent bundle equipped with vertical rescaled Cheeger-Gromoll metric which rescales the vertical part by a non-zero differentiable function $f$. We establish a necessary and sufficient condition under which a covector field is harmonic with respect to this metric. We also construct some examples of harmonic vector fields. Finally, we study the harmonicity of a map between a Riemannian manifold and a cotangent bundle of another Riemannian manifold and vice versa.Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 15(3) (2022), pp. 11-29 |