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Connections in sub-Riemannian geometry of parallelizable distributions

Nabil L. Youssef

Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

E-mail Address: nlyoussef@sci.cu.edu.eg

E-mail Address: nlyoussef2003@yahoo.fr

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and

Ebtsam H. Taha

Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

E-mail Address: ebtsam.taha@sci.cu.edu.eg

E-mail Address: ebtsam.h.taha@hotmail.com

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https://doi.org/10.1142/S0219887817500396Cited by:0 (Source: Crossref)

Abstract

The notion of a parallelizable distribution has been introduced and investigated. A non-integrable parallelizable distribution carries a natural sub-Riemannian structure. The geometry of this structure has been studied from the bi-viewpoint of absolute parallelism geometry and sub-Riemannian geometry. Two remarkable linear connections have been constructed on a sub-Riemannian parallelizable distribution, namely, the Weitzenböck connection and the sub-Riemannian connection. The obtained results have been applied to two concrete examples: the spheres $S^{3}$ and $S^{7}$ .

arXiv: 1603.06106 [math.DG]

Dedicated to the memory of Waleed A. Elsayed

Keywords:

AMSC: 53C17, 58A30, 53C05

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