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

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  • Ludmila Goldberg

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.

Suggested Citation

  • Ludmila Goldberg, 1988. "On singular projective deformations of two second class totally focal pseudocongruences of planes," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:318749
    DOI: 10.1155/S0161171288000110
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