Author/Authors :
Tayyebi ، M. نويسنده Department of pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran , , Heydari، A. نويسنده Department of pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Islamic Republic of Iran ,
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.
