International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 71-80
doi:10.1155/S0161171288000110

On singular projective deformations of two second class totally focal pseudocongruences of planes

Abstract

Let C:L→L¯ be a projective deformation of the second order of two totally focal pseudocongruences L and L¯ of (m−1)-planes in projective spaces Pn and P¯n, 2m−1≤n<3m−1, and let K be a collineation realizing such a C. The deformation C is said to be weakly singular, singular, or α-strongly singular, α=3,4,…, if the collineation K gives projective deformations of order 1, 2 or α of all corresponding focal surfaces of L and L¯. It is proved that C is weakly singular and conditions are found for C to be singular. The pseudocongruences L and L¯ are identical if and only if C is 3-strongly singular.