@article { author = {Tayyebi, M. and Heydari, A.}, title = {Horizontal Subbundle on Lie Algebroids}, journal = {Journal of Sciences, Islamic Republic of Iran}, volume = {27}, number = {3}, pages = {279-285}, year = {2016}, publisher = {University of Tehran}, issn = {1016-1104}, eissn = {2345-6914}, doi = {}, 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.}, keywords = {Lie algebroid,Horizontal subbundle,Double Lie algebroid}, url = {https://jsciences.ut.ac.ir/article_57659.html}, eprint = {https://jsciences.ut.ac.ir/article_57659_592ebb319df73fbbd8a6b864fc3c53cd.pdf} }