Let $ℳ=(M,{𝒪}_{ℳ})$ be a smooth supermanifold with connection $\nabla$ and Batchelor model ${𝒪}_{ℳ}\cong {\Gamma }_{\Lambda E^{*}}$. From $(ℳ,\nabla )$ we construct a connection on the total space of the vector bundle $E\to M$. This reduction of $\nabla$ is well-defined independently of the isomorphism ${𝒪}_{ℳ}\cong {\Gamma }_{\Lambda E^{*}}$. It erases information, but however it turns out that the natural identification of supercurves in $ℳ$ (as maps from ${ℝ}^{1|1}$ to $ℳ$) with curves in $E$ restricts to a 1 to 1 correspondence on geodesics. This bijection is induced by a natural identification of initial conditions for geodesics...