Metric lines in the jet space
In the realm of sub-Riemannian manifolds, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of kk-jets of a real function of one real variable xx, denoted by Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}), admits the structure of a Carnot group. Ever...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-11-01
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| Series: | Analysis and Geometry in Metric Spaces |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/agms-2024-0016 |
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| Summary: | In the realm of sub-Riemannian manifolds, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of kk-jets of a real function of one real variable xx, denoted by Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}), admits the structure of a Carnot group. Every Carnot group is sub-Riemannian manifold, so is Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}). This study aims to present a partial result about the classification of the metric lines within Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}). The method is to use an intermediate three-dimensional sub-Riemannian space RF3{{\mathbb{R}}}_{F}^{3} lying between the group Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}) and the Euclidean space R2{{\mathbb{R}}}^{2}. |
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| ISSN: | 2299-3274 |