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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Main Author: Olena Shugailo
Format: Article
Language:English
Published: Odesa National University of Technology 2024-12-01
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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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
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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