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

View as HTML     View as gif image

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