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On one class of three-webs with covariantly constant curvature and torsion tensors

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Abstract

A special class of multidimensional three-webs \( {W^\nabla } \) with covariantly constant curvature and torsion tensors is considered, the curvature tensor having the minimal rank. It is proved that there is a subfamily of adapted frames of the web \( {W^\nabla } \) whose torsion tensor components are constant and whose curvature tensor has a unique nonzero component. The structure equations of the webs of this class are found and some of their properties are described.

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Authors and Affiliations

  1. Tver State Technical University, Tver, Russia

    L. M. Pidzhakova

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  1. L. M. Pidzhakova
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Correspondence to L. M. Pidzhakova.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 2, pp. 85–91, 2010.

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Pidzhakova, L.M. On one class of three-webs with covariantly constant curvature and torsion tensors. J Math Sci 177, 705–709 (2011). https://doi.org/10.1007/s10958-011-0499-z

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  • DOI: https://doi.org/10.1007/s10958-011-0499-z

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