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

Ludmila Goldberg

International Journal of Mathematics and Mathematical Sciences, 1988, vol. 11, 1-10

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 P n and P ¯ n , 2 m − 1 ≤ n < 3 m − 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.

Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:318749

DOI: 10.1155/S0161171288000110

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