Mappings preserving unit distance on Heisenberg group

J.M. Rassias, A. Charifi, Ab. Chahbi, S. Kabbaj

Let Hm be a Heisenberg group provided with a norm ρ. A mapping f : Hm→ Hm is called preserving the distance n if for all x,y of Hm with ρ(x-1y)=n then ρ(f(x)-1f(y))=n. We obtain some results for the Aleksandrov problem in the Heisenberg group. 

Tbilisi Mathematical Journal, Vol. 8(2) (2015), pp. 131-137