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

[摘要] LetC:L→L¯be a projective deformation of the second order of two totally focal pseudocongruencesLandL¯of(m−1)-planes in projective spacesPnandP¯n,2m−1≤n<3m−1, and letKbe a collineation realizing such aC. The deformationCis said to be weakly singular, singular, orα-strongly singular,α=3,4,…, if the collineationKgives projective deformations of order1,2orαof all corresponding focal surfaces ofLandL¯. It is proved thatCis weakly singular and conditions are found forCto be singular. The pseudocongruencesLandL¯are identical if and only ifCis3-strongly singular.

[学科分类] 数学（综合）