Geodesics and submanifold structures in conformal geometry

A conformal structure on a manifold M-n induces natural second order conformally invariant operators, called Mobius and Laplace structures, acting on specific weight bundles of M, provided that n >= 3. By extending the notions of Mobius 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. (C) 2015 Elsevier B.V. All rights reserved.