Invariants of conformal embeddings

We define some tensorial quantities characterizing locally a conformal embdedding. The vanishing of these invariants defines various notions of conformal geodesy that are usually very restrictive if the ambient space is fixed. For a conformally geodesic embedding of a conformally flat manifold into an Euclidean space, there is no local restriction, but we exhibit global obstructions based on the structure induced on curves.