Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012
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On curve based ruled affine submanifolds

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Olena Shugailo
http://orcid.org/0000-0002-1238-3403

Abstract

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.

Keywords:
affine immersion, equiaffine structure, ruled submanifild, flat connection

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How to Cite
Shugailo, O. (2024). On curve based ruled affine submanifolds. Proceedings of the International Geometry Center, 17(3), 203-217. https://doi.org/10.15673/pigc.v17i3.2883
Section
Papers
Author Biography

Olena Shugailo, V. N. Karazin Kharkiv National University

Department of Pure Mathematics