Horizontal Subbundle on Lie Algebroids - M. Tayyebi; A. Heydari (Journal of Sciences, Islamic Republic of Iran)
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.