Russian Mathematics

, Volume 62, Issue 11, pp 45–52 | Cite as

The Contact Metric Connection on the Heisenberg Group

  • V. I. Pan’zhenskiiEmail author
  • T. R. Klimova


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.


Heisenberg group Sasakian structure connection with skew-torsion sectional curvature 


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© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Pedagogical Institute named after V. G. BelinskiiPenzaRussia

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