International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 71-80
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.
Let be a projective deformation of the second order of two totally focal pseudocongruences and of -planes in projective spaces and , , and let be a collineation realizing such a . The deformation is said to be weakly singular, singular, or -strongly singular, , if the collineation gives projective deformations of order , or of all corresponding focal surfaces of and . It is proved that is weakly singular and conditions are found for to be singular. The pseudocongruences and are identical if and only if is -strongly singular.