RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Sibirsk. Mat. Zh.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Sibirsk. Mat. Zh., 2017, Volume 58, Number 6, Pages 1218–1227 (Mi smj2932)  

On a certain sub-Riemannian geodesic flow on the Heisenberg group

S. V. Agapovab, M. R. Borchashvilib

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: Under study is an integrable geodesic flow of a left-invariant sub-Riemannian metric for a right-invariant distribution on the Heisenberg group. We obtain the classification of the trajectories of this flow. There are a few examples of trajectories in the paper which correspond to various values of the first integrals. These trajectories are obtained by numerical integration of the Hamiltonian equations. It is shown that for some values of the first integrals we can obtain explicit formulae for geodesics by inverting the corresponding Legendre elliptic integrals.

Keywords: sub-Riemannian geometry, geodesic flow, left-invariant metric.

Funding Agency Grant Number
Russian Science Foundation 14-11-00441
The authors were supported by the Russian Science Foundation (Grant 14-11-00441).


DOI: https://doi.org/10.17377/smzh.2017.58.603

Full text: PDF file (316 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2017, 58:6, 943–951

Bibliographic databases:

UDC: 517.977
MSC: 35R30
Received: 17.07.2017

Citation: S. V. Agapov, M. R. Borchashvili, “On a certain sub-Riemannian geodesic flow on the Heisenberg group”, Sibirsk. Mat. Zh., 58:6 (2017), 1218–1227; Siberian Math. J., 58:6 (2017), 943–951

Citation in format AMSBIB
\Bibitem{AgaBor17}
\by S.~V.~Agapov, M.~R.~Borchashvili
\paper On a~certain sub-Riemannian geodesic flow on the Heisenberg group
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 6
\pages 1218--1227
\mathnet{http://mi.mathnet.ru/smj2932}
\crossref{https://doi.org/10.17377/smzh.2017.58.603}
\elib{http://elibrary.ru/item.asp?id=30556269}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 6
\pages 943--951
\crossref{https://doi.org/10.1134/S0037446617060039}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000425153500003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042150619}


Linking options:
  • http://mi.mathnet.ru/eng/smj2932
  • http://mi.mathnet.ru/eng/smj/v58/i6/p1218

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Сибирский математический журнал Siberian Mathematical Journal
    Number of views:
    This page:177
    Full text:38
    References:22
    First page:13

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019