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The Contact Metric Connection with Skew Torsion

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Abstract

We prove that, on a generalized (multidimensional) Heisenberg group endowed with a left-invariant Sasakian structure, there exists a unique contact metric connection with skew torsion, invariant with respect to the group of automorphisms. The explicit expression of this connection in terms of the contact form and the metric tensor is obtained. It is shown that the torsion tensor and the curvature tensor are covariantly constant, and the sectional curvature varies between —1 and 0. It is proved that the obtained connection is a contact metric connection for any k-contact metric structure, therefore it is a contact metric connection for any Sasakian structure.

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Authors and Affiliations

  1. Penza State University, 37 Lermontov str., Penza, 440026, Russia

    V. I. Panzhenskii & T. R. Klimova

Authors
  1. V. I. Panzhenskii
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  2. T. R. Klimova
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Correspondence to V. I. Panzhenskii or T. R. Klimova.

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Russian Text © The Author(s), 2019, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, No. 11, pp. 54–63.

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Panzhenskii, V.I., Klimova, T.R. The Contact Metric Connection with Skew Torsion. Russ Math. 63, 47–55 (2019). https://doi.org/10.3103/S1066369X19110070

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  • DOI: https://doi.org/10.3103/S1066369X19110070

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