FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 1, PAGES 121-133

**Three-webs with covariantly constant curvature and torsion tensors**

L. M. Pidzhakova

Abstract

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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 homogeneous space $G/H$ carrying the
$3$-web is
described.
Structure equations of $G$-group are found.
In the second part, we have found structure equations of $W$Ñ-web and finite
equations of some special web classes.

Location: http://mech.math.msu.su/~fpm/eng/k10/k101/k10110h.htm

Last modified: March 11, 2011