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
Department of Mathematics, New Jersey Institute of Technology, Newark 07102, New Jersey, USA
Received 31 July 1986
Copyright © 1988 Ludmila Goldberg. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.