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The Contact Metric Connection on the Heisenberg Group

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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 via 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.

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Authors and Affiliations

  1. Pedagogical Institute named after V. G. Belinskii, ul. Lermontova 37, Penza, 440026, Russia

    V. I. Pan’zhenskii & T. R. Klimova

Authors
  1. V. I. Pan’zhenskii
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  2. T. R. Klimova
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Corresponding author

Correspondence to V. I. Pan’zhenskii.

Additional information

Original Russian Text © V.I. Pan’zhenskii, T.R. Klimova, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 11, pp. 51–59.

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Pan’zhenskii, V.I., Klimova, T.R. The Contact Metric Connection on the Heisenberg Group. Russ Math. 62, 45–52 (2018). https://doi.org/10.3103/S1066369X18110051

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  • DOI: https://doi.org/10.3103/S1066369X18110051

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