1
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
2
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Abstract
In this paper, we introduce the structure of a groupoid associated to a vector field on a smooth manifold. We show that in the case of the $1$-dimensional manifolds, our groupoid has a smooth structure such that makes it into a Lie groupoid. Using this approach, we associated to every vector field an equivalence relation on the Lie algebra of all vector fields on the smooth manifolds.
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