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On a problem of Chern-Akivis-Shelekhov on hexagonal three-webs. (English) Zbl 0845.53011
As is proved in [the reviewer, J. Sov. Math. 44, No. 2, 153-190 (1989; Zbl 0711.53013)], any multidimensional hexagonal 3-web $$W$$ has the 4th-order closed structure (in the sense of M. A. Akivis), that is the second-order (covariant) derivatives of the curvature tensor $$b$$ of $$W$$ can be expressed in terms of the tensors $$a$$ (torsion), $$b$$ and the first-order derivatives of $$b$$. In the paper under review, the corresponding relations are found in an explicit form. To obtain these relations, the author rewrites the structure equations of a hexagonal 3-web in a more laconic and convenient form. As a result, all 4th-order tensors can be expressed in terms of only one of them.

##### MSC:
 53A60 Differential geometry of webs 20N05 Loops, quasigroups
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##### References:
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