On a problem of Chern-Akivis-Shelekhov on hexagonal three-webs
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.
scientific article; zbMATH DE number 856821