Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids

Abstract

Given a strictly pseudoconvex hypersurface M ⊂ Cⁿ⁺¹, we discuss the problem of classifying all local CR diffeomorphisms between open subsets N, N′ ⊂ M. Our method exploits the Tanaka-Webster pseudohermitian invariants of a contact form ϑ on M, their transformation formulae, and the Chern-Moser invariants. Our main application concerns a class of generalized ellipsoids where we classify all local CR mappings.