Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids

We discuss the problem of classifying all local CR diffeomorphisms of a strictly pseudoconvex surface. Our method exploits the Tanaka–Webster pseudohermitian invariants, their transformation formulae, and the Chern–Moser invariants. Our main application concerns a class of generalized ellipsoids where we classify all local CR mappings.