RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Vyssh. Uchebn. Zaved. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. Vyssh. Uchebn. Zaved. Mat., 2018, Number 11, Pages 51–59 (Mi ivm9412)  

The contact metric connection on the Heisenberg group

V. I. Panzhenskii, T. R. Klimova

Pedagogical Institute named after V.G. Belinskii, 37 Lermontov str., Penza, 440026 Russia

Abstract: We prove that there is only one contact metric connection with skew-torsion on the Heisenberg group endowed with a left-invariant Sasakian structure. We obtain the expression of this connection through the contact form and the metric tensor and show that the torsion tensor and the curvature tensor are constant and the sectional curvature varies between $-1$ and $0$.

Keywords: Heisenberg group, Sasakian structure, connection with skew-torsion, sectional curvature.

Full text: PDF file (191 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 514.763
Received: 31.10.2017

Citation: V. I. Panzhenskii, T. R. Klimova, “The contact metric connection on the Heisenberg group”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 11, 51–59

Citation in format AMSBIB
\Bibitem{PanKli18}
\by V.~I.~Panzhenskii, T.~R.~Klimova
\paper The contact metric connection on the Heisenberg group
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2018
\issue 11
\pages 51--59
\mathnet{http://mi.mathnet.ru/ivm9412}


Linking options:
  • http://mi.mathnet.ru/eng/ivm9412
  • http://mi.mathnet.ru/eng/ivm/y2018/i11/p51

    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
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
    Number of views:
    This page:34
    References:4
    First page:4

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