Geodesics and Conformal Transformations of Heisenberg-Reiter Spaces

Abstract

Generalized Heisenberg groups, in the sense of Reiter, can be endowed with left-invariant metrics whose geodesies and curvature are obtained. Using these curvature data it is also proved that on their nilmanifolds (compact or not), every conformai transformation is in fact an isometry. A large family of nonisometric examples is given.