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Three-webs with covariantly constant curvature and torsion tensors

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Abstract

In this paper, we study a special class of multidimensional 3-webs with covariantly constant curvature and torsion tensors. In the first part, we prove that 3-webs of the class belong to G-webs, i.e., there is a subfamily of adapted frames whose components of curvature and torsion tensors are constant. The structure of the homogeneous space G/H carrying the 3-web is described. Structure equations of the G-group are found. In the second part, we find structure equations of the W ▽-web and finite equations of some special web classes.

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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. 1, pp. 121–133, 2010.

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Pidzhakova, L.M. Three-webs with covariantly constant curvature and torsion tensors. J Math Sci 177, 597–606 (2011). https://doi.org/10.1007/s10958-011-0485-5

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