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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Geodesic Reduction via Frame Bundle Geometry
Ajit Bhand Department of Mathematics, University of Oklahoma, Norman, OK, USA
Аннотация:
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.
Ключевые слова:
affine connection; geodesic spray; reduction; linear frame bundle.
Поступила: 12 октября 2009 г.; в окончательном варианте 18 февраля 2010 г.; опубликована 22 февраля 2010 г.
Образец цитирования:
Ajit Bhand, “Geodesic Reduction via Frame Bundle Geometry”, SIGMA, 6 (2010), 020, 17 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma477 https://www.mathnet.ru/rus/sigma/v6/p20
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