Conformality of a differential with respect to Cheeger-Gromoll type metrics

Abstract

We investigate conformality of the differential of a mapping between Riemannian manifolds if the tangent bundles are equipped with a generalized metric of CheegerGromoll type.

Differential as a harmonic morphism with respect to Cheeger–Gromoll-type metrics

“…These metrics h p,q , depending on two constants p, q, generalize the Sasaki and Cheeger-Gromoll metrics. A wider class of this type of metrics was investigated by Munteanu [10] and by the authors [8]. Now, there are several articles concerning geometry of a tangent bundle equipped with a Cheeger-Gromoll-type metric.…”

“…In [8], the authors studied the conformality of a differential = ϕ * : TM,h → (TN, h) of a map ϕ: M → N between Riemannian manifolds, whereh = h p,q,α and h = h r,s,β are metrics of Cheeger-Gromoll type. In this article, we continue considerations concerning the differential of a map.…”