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On the closed G-structure associated to a hexagonal 3-web. (English) Zbl 0699.53024
Differential geometry and its applications, Proc. Conf., Dubrovnik/Yugosl. 1988, 323-326 (1989).
[For the entire collection see Zbl 0679.00010.]
The author announces the following result: A G-structure associated with a hexagonal 3-web W of codimension r given on (2r)-dimensional differentiable manifold is a closed G-structure of 4th order. This problem was posed by M. A. Akivis [see Itogi Nauki Tekh., Ser. Probl. Geom. 7, 69-79 (1975; Zbl 0549.53032)] solved by V. P. Botsu for \(r=2\) [On the isoclinical property of four-dimensional hexagonal three-webs. Deposited scientific paper - VINITI 5824-84, 27 p. (1984)]. The author’s proof valid for any r can be found in his paper [J. Geom. 35, No.1/2, 169-176 (1989; see the next review)] and [Itogi Nauki Tekh., Ser. Probl. Geom. 19, 101-154; VINITI Akad. Nauk SSSR (Moscow, 1987)].
Reviewer: V.V.Goldberg
MSC:
53A60 Differential geometry of webs
53C10 \(G\)-structures