Mappings preserving unit distance on Heisenberg group

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

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Bibliographic Details
Published inTbilisi Mathematical Journal Vol. 8; no. 2
Main Authors Rassias, J.M., Charifi, A., Chahbi, Ab, Kabbaj, S.
Format Journal Article
LanguageEnglish
Published De Gruyter Open 01.12.2015
Subjects
conservative distance
Isometry
Lipschitz mapping
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Summary:Let H be a Heisenberg group provided with a norm ρ. A mapping ƒ : H → H is called preserving the distance n if for all x, y of H with ρ(x y) = n then ρ(f(x) ƒ(y)) = n. We obtain some results for the Aleksandrov problem in the Heisenberg group.
ISSN:1875-158X
1512-0139
DOI:10.1515/tmj-2015-0016