Geodesics and submanifold structures in conformal geometry

A conformal structure on a manifold MnMn induces natural second order conformally invariant operators, called Möbius and Laplace structures, acting on specific weight bundles of MM, provided that n≥3n≥3. By extending the notions of Möbius and Laplace structures to the case of surfaces and curves, we develop here the theory of extrinsic conformal geometry for submanifolds, find tensorial invariants of a conformal embedding, and use these invariants to characterize various notions of geodesic submanifolds.