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Geodesic Reduction via Frame Bundle Geometry
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6, випуск за цей рік
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Geodesic Reduction via Frame Bundle Geometry
Інший ID:
2010 Mathematics Subject Classification: 53B05; 53C05; 53C22; 58D19
DOI:10.3842/SIGMA.2010.020
DOI:10.3842/SIGMA.2010.020
Посилання:
Geodesic Reduction via Frame Bundle Geometry / A. Bhand // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 22 назв. — англ.
Підтримка:
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.
Дата:
2010
Переглядів:
437
Завантажень:
236
Анотація:
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.
