On the geometry of the (2n+1)-webs in \(2n\)-dimensional affinely connnected spaces \(A_{2n}\) (Q1173715)

The geometry of \((2n+1)\)-webs being formed by families of curves in affinely connected spaces \(A_{2n}\) is studied by the method of extended differentiation [\textit{A. P. Norden}, Affinely connected spaces, 2nd ed. (Moscow 1976); 1st ed. Moscow (1950; Zbl 0041.50201)]. On a \((2n+1)\)-web the tensors \(b^{ik}\), \(b_{ik}\) and \(b^k_i\), called Hesse tensors, with weights \(2, -2\) and \(0\) respectively are defined in an invariant way. The properties of Hesse tensors of \((2n+1)\)-webs are studied. In particular the webs are considered on which these tensors are covariantly constant.