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All Journal Hipotenusa: Journal of Research Mathematics Education (HJRME)
Dieumerci Matumona
University of Kinshasa, Faculty of Sciences, Department of Mathematics and Computer Science
Education Mathematics Other

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TOTALLY NONHOLONOMIC DISTRIBUTIONS AND SUB-RIEMANNIAN STRUCTURES Michael Makiese Kilela; Oscar Lungiambudila; Joel Kabuya; Dieumerci Matumona
Hipotenusa Journal of Research Mathematics Education (HJRME) Vol 7, No 1 (2024): Hipotenusa Journal of Research Mathematics Education (HJRME)
Publisher : Universitas Muhammadiyah Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.36269/hjrme.v7i1.2178

Abstract

In this paper, we study totally non-holonomic distributions and sub-riemannian structure on Rn (n = 1, 2, 3, 4, ...) and on the manifolds of not null curvature such as Tn  and Sn with n more or equal than 3, in order to look at this structure on a manifold like a restricting of a Riemannian metric on a totally non-holonomic distribution of this manifold. On Rn, it always possible to construct this structure thanks to her multitude of smooth distributions and vector elds. On the manifolds of not null curvature, we de ne this structure on the kernel of a non-degenerate 1-form or of contact form on this manifold.
Co-Authors Joel Kabuya Michael Makiese Kilela Oscar Lungiambudila