Families \(V_{2n-1}^2\) and \(U_{2n-1}^m\) and their projective deformations (Q1397585)

Certain classes of families \(L^m_{2n-1}\) are considered in this paper. The family \(V^2_{2n-1}\) is a generalization of a congruence \(V\) and the family \(U^m_{2n-1}\) a generalization of a line congruence. A constructive description of the family \(U^m_{2n-1}\) is given. The problem of projective bendings of these families is studied. Of special interest, from our point of view, is theorem 3: The family \(U^n_{2n-1}\) depends on \(4n(n-1)\) arbitrary constants. The paper contains a series of interesting results and ten theorems. Most of them are given with detailed proofs. The table of references has 4 items.