The geodesic flow on a Riemannian supermanifold

International audienceWe give a natural definition of geodesics on a Riemannian supermanifold (M, g) and extend the usual geodesic flow on T * M associated to the underlying Rieman-nian manifold (M, g) to a geodesic " superflow " on T * M. Integral curves of this flow turn out to be in natural bijection with geodesics on M. We also construct the corresponding exponential map and generalize the well-known faithful linearization of isometries to Riemannian supermanifolds