Geodesic Reduction via Frame Bundle Geometry
A manifold with an arbitrary affine connection is considered and the geodesic spray associated with the connection is studied in the presence of a Lie group action. In particular, results are obtained that provide insight into the structure of the reduced dynamics associated with the given invariant...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2010 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2010
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146313 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Geodesic Reduction via Frame Bundle Geometry / A. Bhand // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862616820514553856 |
|---|---|
| author | Bhand, A. |
| author_facet | Bhand, A. |
| citation_txt | Geodesic Reduction via Frame Bundle Geometry / A. Bhand // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A manifold with an arbitrary affine connection is considered and the geodesic spray associated with the connection is studied in the presence of a Lie group action. In particular, results are obtained that provide insight into the structure of the reduced dynamics associated with the given invariant affine connection. The geometry of the frame bundle of the given manifold is used to provide an intrinsic description of the geodesic spray. A fundamental relationship between the geodesic spray, the tangent lift and the vertical lift of the symmetric product is obtained, which provides a key to understanding reduction in this formulation.
|
| first_indexed | 2025-12-07T13:10:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146313 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T13:10:08Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bhand, A. 2019-02-08T20:28:17Z 2019-02-08T20:28:17Z 2010 Geodesic Reduction via Frame Bundle Geometry / A. Bhand // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53B05; 53C05; 53C22; 58D19 DOI:10.3842/SIGMA.2010.020 https://nasplib.isofts.kiev.ua/handle/123456789/146313 A manifold with an arbitrary affine connection is considered and the geodesic spray associated with the connection is studied in the presence of a Lie group action. In particular, results are obtained that provide insight into the structure of the reduced dynamics associated with the given invariant affine connection. The geometry of the frame bundle of the given manifold is used to provide an intrinsic description of the geodesic spray. A fundamental relationship between the geodesic spray, the tangent lift and the vertical lift of the symmetric product is obtained, which provides a key to understanding reduction in this formulation. I would like to thank my thesis supervisor Dr. Andrew Lewis for his constant guidance and support. This work would not have materialized without the many invaluable discussions I have had with him over the years. The author also thanks the anonymous referees for their constructive comments on a previous version of this paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Geodesic Reduction via Frame Bundle Geometry Article published earlier |
| spellingShingle | Geodesic Reduction via Frame Bundle Geometry Bhand, A. |
| title | Geodesic Reduction via Frame Bundle Geometry |
| title_full | Geodesic Reduction via Frame Bundle Geometry |
| title_fullStr | Geodesic Reduction via Frame Bundle Geometry |
| title_full_unstemmed | Geodesic Reduction via Frame Bundle Geometry |
| title_short | Geodesic Reduction via Frame Bundle Geometry |
| title_sort | geodesic reduction via frame bundle geometry |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146313 |
| work_keys_str_mv | AT bhanda geodesicreductionviaframebundlegeometry |