On a problem of Chern-Akivis-Shelekhov on hexagonal three-webs

In the following we discuss the infinitesimal theory of analytic multidimensional hexagonal three-webs. It is known that the structure of any such three-web in a neighborhood of an arbitrary point is uniquely determined by four tensor values at the given point. We prove that three of them are sufficient and we analyze the corresponding integrability conditions. © 1996 Birkhäuser Verlag.