Let $(M,g)$ be a Riemannian manifold and $\nabla$ be the Levi-Civita connection of $g$ and let $X,Y$ be vector fields on $M$. If $\lbrace \phi _t \rbrace $ is the 1-parameter group of $X$ then what is the relation between $\nabla _YX$ and $\phi _{t*}Y$($\phi _{t*}$ is the differential of $\phi _t$)?