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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| Format: | Article |
| Language: | English |
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Wiley
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171288000110 |
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| _version_ | 1832563074464219136 |
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| author | Ludmila Goldberg |
| author_facet | Ludmila Goldberg |
| author_sort | Ludmila Goldberg |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-38485e0db5324e7b8106f7116b5d8bb1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1988-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-38485e0db5324e7b8106f7116b5d8bb12025-02-03T01:20:59ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251988-01-01111718010.1155/S0161171288000110On singular projective deformations of two second class totally focal pseudocongruences of planesLudmila Goldberg0Department of Mathematics, New Jersey Institute of Technology, Newark 07102, New Jersey, USALet 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.http://dx.doi.org/10.1155/S0161171288000110pseudocongruenceprojective deformationsingular projective deformationfocal surface. |
| spellingShingle | Ludmila Goldberg On singular projective deformations of two second class totally focal pseudocongruences of planes International Journal of Mathematics and Mathematical Sciences pseudocongruence projective deformation singular projective deformation focal surface. |
| title | On singular projective deformations of two second class totally focal pseudocongruences of planes |
| title_full | On singular projective deformations of two second class totally focal pseudocongruences of planes |
| title_fullStr | On singular projective deformations of two second class totally focal pseudocongruences of planes |
| title_full_unstemmed | On singular projective deformations of two second class totally focal pseudocongruences of planes |
| title_short | On singular projective deformations of two second class totally focal pseudocongruences of planes |
| title_sort | on singular projective deformations of two second class totally focal pseudocongruences of planes |
| topic | pseudocongruence projective deformation singular projective deformation focal surface. |
| url | http://dx.doi.org/10.1155/S0161171288000110 |
| work_keys_str_mv | AT ludmilagoldberg onsingularprojectivedeformationsoftwosecondclasstotallyfocalpseudocongruencesofplanes |