A lossless reduction of geodesics on supermanifolds to non-graded differential geometry

Stéphane Garnier, Matthias Kalus

Let $\mathcal{M}=(M,{\mathcal{O}}_{\mathcal{M}})$ be a smooth supermanifold with connection $\nabla$ and Batchelor model ${\mathcal{O}}_{\mathcal{M}}\cong {\Gamma }_{\Lambda E^{\ast }}$. From $(\mathcal M,\nabla…