FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 2, PAGES 85-91

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

L. M. Pidzhakova

Abstract

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A special class of multidimensional three-webs $W$Ñ 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 $W$Ñ whose torsion tensor components are constant and the 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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