Torsionless And The Structure Of The Lie Algebroid Commutative Lie Algebroid Contact And Its Nature

In this paper, we will mainly discuss the Lie Algebroid connection including some properties and applications of it. And we will also prove the existance of torsion free and compatible with Lie Algebroid structure A-connection.Then we will introduce some other properties of A-connection.The paper can be divided into four chapters .The first one is the introduction.In the second chapter we will introduce some basic knowlege of Lie Algebroid as the preparetion for the next two chapters.In the third chapter we will introduce the Lie-Algebroid connection and some related contents .The fourth chapter is about the Lie Algebroid holonomy. In this chapter we will introduce the conception of A-holonomy. we will study some properties of Lie Algebroid under the basis of it .