On curve based ruled affine submanifolds
In this paper we consider affine ruled submanifolds of arbitrary dimension and codimension in the classical sense, i.e. curve based ones. For such a submanifold we define the natural parameterization and the natural transversal distribution. We calculate all the affine characteristics for such an af...
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| Format: | Article |
| Language: | English |
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Odesa National University of Technology
2024-12-01
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| Series: | Pracì Mìžnarodnogo Geometričnogo Centru |
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| Online Access: | https://journals.ontu.edu.ua/index.php/geometry/article/view/2883 |
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| _version_ | 1846143524013080576 |
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| author | Olena Shugailo |
| author_facet | Olena Shugailo |
| author_sort | Olena Shugailo |
| collection | DOAJ |
| description | In this paper we consider affine ruled submanifolds of arbitrary dimension and codimension in the classical sense, i.e. curve based ones. For such a submanifold we define the natural parameterization and the natural transversal distribution. We calculate all the affine characteristics for such an affine immersion. We find conditions on the base curve and the directions of the rectilinear generators such that the induced connection is flat and the natural transversal distribution is equiaffine. |
| format | Article |
| id | doaj-art-aba2a03cfee94854bb6c90291f584cfb |
| institution | Kabale University |
| issn | 2072-9812 2409-8906 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Odesa National University of Technology |
| record_format | Article |
| series | Pracì Mìžnarodnogo Geometričnogo Centru |
| spelling | doaj-art-aba2a03cfee94854bb6c90291f584cfb2024-12-02T12:32:14ZengOdesa National University of TechnologyPracì Mìžnarodnogo Geometričnogo Centru2072-98122409-89062024-12-0117320321710.15673/pigc.v17i3.28832883On curve based ruled affine submanifoldsOlena Shugailo0V. N. Karazin Kharkiv National UniversityIn this paper we consider affine ruled submanifolds of arbitrary dimension and codimension in the classical sense, i.e. curve based ones. For such a submanifold we define the natural parameterization and the natural transversal distribution. We calculate all the affine characteristics for such an affine immersion. We find conditions on the base curve and the directions of the rectilinear generators such that the induced connection is flat and the natural transversal distribution is equiaffine.https://journals.ontu.edu.ua/index.php/geometry/article/view/2883affine immersionequiaffine structureruled submanifildflat connection |
| spellingShingle | Olena Shugailo On curve based ruled affine submanifolds Pracì Mìžnarodnogo Geometričnogo Centru affine immersion equiaffine structure ruled submanifild flat connection |
| title | On curve based ruled affine submanifolds |
| title_full | On curve based ruled affine submanifolds |
| title_fullStr | On curve based ruled affine submanifolds |
| title_full_unstemmed | On curve based ruled affine submanifolds |
| title_short | On curve based ruled affine submanifolds |
| title_sort | on curve based ruled affine submanifolds |
| topic | affine immersion equiaffine structure ruled submanifild flat connection |
| url | https://journals.ontu.edu.ua/index.php/geometry/article/view/2883 |
| work_keys_str_mv | AT olenashugailo oncurvebasedruledaffinesubmanifolds |