On singular projective deformations of two second class totally focal pseudocongruences of planes
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 singula...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171288000110 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |