… Let Torn be an n-dimensional torus with a Riemannian metric d which does not have
conjugate points. Then d is a … We consider a Riemannian metric don Rn which is a lift of
some metric d on Torn = Rn/Zn. Thus dis invariant under the action of Zn by integer
translations. We denote by UTTorn and UTRn the unit tangent bundles for metrics d and d. …
Hereafter, we assume that d does not have conjugate points and hence the length of every
geodesic segment is just the distance between its endpoints. For (x, v) ∈ UTRn we define …