Horizontal Subbundle on Lie Algebroids
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Abstract:
Providing an appropriate definition of a horizontal subbundle of a Lie algebroid will lead to construction of a better framework on Lie algebriods. In this paper, we give a new and natural definition of a horizontal subbundle using the prolongation of a Lie algebroid and then we show that any linear connection on a Lie algebroid generates a horizontal subbundle and vice versa. The same correspondence will be proved for any covariant derivative on a Lie algebroid.
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Journal title
volume 27 issue 3
pages 279- 285
publication date 2016-07-01
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