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 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.

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Document Type: Article
UDC: 514.763

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}