Vertical rescaled CheegerGromoll metric and harmonicity on the cotangent bundle
A. Zagane, A. Gezer
In this paper, we introduce the harmonicity on the cotangent bundle equipped
with vertical rescaled CheegerGromoll metric which rescales the vertical
part by a nonzero 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: EuroTbilisi Mathematical Journal, Vol. 15(3) (2022), pp. 1129
