We consider Heisenberg groups equipped with a sub-Finsler metric. Using methods of optimal control theory we prove that in this geometric setting the infinite geodesics are horizontal lines under the assumption that the sub-Finsler metric is defined by a strictly convex norm. This answers a question posed in [8] and has applications in the characterization of isometric embeddings into Heisenberg groups.

Balogh, Z., Calogero, A. (2021). Infinite Geodesics of Sub-Finsler Distances in Heisenberg Groups. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2021(7), 4805-4837 [10.1093/imrn/rnz074].

Infinite Geodesics of Sub-Finsler Distances in Heisenberg Groups

Calogero, A
2021

Abstract

We consider Heisenberg groups equipped with a sub-Finsler metric. Using methods of optimal control theory we prove that in this geometric setting the infinite geodesics are horizontal lines under the assumption that the sub-Finsler metric is defined by a strictly convex norm. This answers a question posed in [8] and has applications in the characterization of isometric embeddings into Heisenberg groups.
Articolo in rivista - Articolo scientifico
Heisenberg group, homogeneous norms, geodesics, optimal control;
English
9-apr-2019
2021
2021
7
4805
4837
rnz074
partially_open
Balogh, Z., Calogero, A. (2021). Infinite Geodesics of Sub-Finsler Distances in Heisenberg Groups. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2021(7), 4805-4837 [10.1093/imrn/rnz074].
File in questo prodotto:
File Dimensione Formato  
rnz074.pdf

Solo gestori archivio

Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Dimensione 442.39 kB
Formato Adobe PDF
442.39 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
infinite geodesic BALOGH_CALOGERO.pdf

accesso aperto

Tipologia di allegato: Submitted Version (Pre-print)
Dimensione 319.55 kB
Formato Adobe PDF
319.55 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/258911
Citazioni
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
Social impact