Given a strictly pseudoconvex hypersurface M ½ Cn+1, we discuss the problem of classifying all local CR diffeomorphisms between open subsets N;N0 ½ M. Our method exploits the Tanaka–Webster pseudohermitian invariants of a contact form # 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.
Pseudohermitian invariants and classification of CR mappings in generalized ellipsoids
MONTI, ROBERTO;
2012
Abstract
Given a strictly pseudoconvex hypersurface M ½ Cn+1, we discuss the problem of classifying all local CR diffeomorphisms between open subsets N;N0 ½ M. Our method exploits the Tanaka–Webster pseudohermitian invariants of a contact form # 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.
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