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Left-invariant sub-Riemannian structures on a five-dimensional two-step nilpotent Lie group: isometries, classification, and geodesics
Dissertation (MSc)--University of Pretoria, 2021.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2021
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| _version_ | 1867613590687580160 |
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| access_status_str | Open Access |
| author2 | Biggs, Rory |
| author_browse | Biggs, Rory |
| author_facet | Biggs, Rory |
| collection | Thesis |
| dc_rights_str_mv | © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc)--University of Pretoria, 2021. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/80760 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:34.370Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/80760 Left-invariant sub-Riemannian structures on a five-dimensional two-step nilpotent Lie group: isometries, classification, and geodesics Biggs, Rory ontshudisane@yahoo.com Ntshudisane, Odirile Mathematics UCTD Dissertation (MSc)--University of Pretoria, 2021. In this dissertation we study a five-dimensional two-step nilpotent matrix Lie group. Some basic group properties are investigated. The structure of the Lie algebra’s subspaces is investigated; a complete set of scalar invariants is given for the Lie algebra’s subspace structure. Following this, we classify the left-invariant sub-Riemannian structures on this Lie group up to isometry. The normal geodesics of the rank three left-invariant sub-Riemannian structure are determined as an illustrative case. Mathematics and Applied Mathematics MSc Restricted 2021-07-09T12:52:20Z 2021-07-09T12:52:20Z 2021 2021 Dissertation * S2021 http://hdl.handle.net/2263/80760 en © 2019 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | Mathematics UCTD Left-invariant sub-Riemannian structures on a five-dimensional two-step nilpotent Lie group: isometries, classification, and geodesics |
| title | Left-invariant sub-Riemannian structures on a five-dimensional two-step nilpotent Lie group: isometries, classification, and geodesics |
| title_full | Left-invariant sub-Riemannian structures on a five-dimensional two-step nilpotent Lie group: isometries, classification, and geodesics |
| title_fullStr | Left-invariant sub-Riemannian structures on a five-dimensional two-step nilpotent Lie group: isometries, classification, and geodesics |
| title_full_unstemmed | Left-invariant sub-Riemannian structures on a five-dimensional two-step nilpotent Lie group: isometries, classification, and geodesics |
| title_short | Left-invariant sub-Riemannian structures on a five-dimensional two-step nilpotent Lie group: isometries, classification, and geodesics |
| title_sort | left invariant sub riemannian structures on a five dimensional two step nilpotent lie group isometries classification and geodesics |
| topic | Mathematics UCTD |
| url | http://hdl.handle.net/2263/80760 |