This article is cited in 1 paper

Bol three-webs with covariant constant curvature tensor

A. M. Shelekhov^a, E. A. Onoprienko<sup>b

a</sup> Chair of Functional Analysis and Geometry, Tver State University, 33 Zhelyabova str., Tver, 170100 Russia
^b Chair of Geometry, Moscow Pedagogical State University, 1 M. Pirogovskaya str., Moscow, 119991 Russia

Abstract: We find complete system of tensor relations characterizing the class of multidimensional middle Bol three-webs with covariant constant curvature tensor and ascertain the algebraic sense of these relations. We prove the existence of such webs and lay the foundation of their classification in terms of torsion tensor rank. We show that $6$-dimensional non-group webs of such type are the known flexible webs $E_1$ and $E_2$.

Keywords: three-web, middle Bol three-web, flexible three-web, $W$-algebra, Chern connection of a three-web, commutator, associator, holonomy algebra.

UDC: 514.763

Received: 18.08.2014

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:3, 72–81

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