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...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2010
1. Verfasser: Bhand, A.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2010
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146313
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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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
Beschreibung
Zusammenfassung: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.
ISSN:1815-0659