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

This article is cited in 3 scientific papers (total in 3 papers)

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)
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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}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Panzhenskii, T. R. Klimova, “The contact metric connection with skew torsion”, Russian Math. (Iz. VUZ), 63:11 (2019), 47–55  mathnet  crossref  crossref  isi
    2. V. I. Panzhenskii, O. P. Surina, “Subrimanovy geodezicheskie na mnogomernoi gruppe Geizenberga”, Trudy mezhdunarodnoi konferentsii Klassicheskaya i sovremennaya geometriya, posvyaschennoi 100-letiyu so dnya rozhdeniyaprofessora Vyacheslava Timofeevicha Bazyleva. Moskva, 2225 aprelya 2019 g. Chast 2, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 180, VINITI RAN, M., 2020, 74–84  mathnet  crossref
    3. V. I. Panzhenskii, A. O. Rastrepina, “Levoinvariantnaya kontaktnaya metricheskaya struktura na mnogoobrazii Sol”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 162, no. 1, Izd-vo Kazanskogo un-ta, Kazan, 2020, 77–90  mathnet  crossref
  •    . Russian Mathematics (Izvestiya VUZ. Matematika)
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