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Diffeomorphisms preserving R ‐circles in three dimensional CR manifolds
Author(s) -
Falbel E.,
Veloso J. M.
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400301
Subject(s) - diffeomorphism , geodesic , manifold (fluid mechanics) , pure mathematics , mathematics , conjugate points , boundary (topology) , degenerate energy levels , space (punctuation) , mathematical analysis , physics , computer science , mechanical engineering , quantum mechanics , engineering , operating system
R ‐circles in (non‐degenerate) three dimensional CR manifolds are the analogues to traces of Lagrangian totally geodesic planes on S 3 viewed as the boundary of two dimensional complex hyperbolic space. They form a family of certain Legendrian curves on the manifold. We prove that a diffeomorphism between three dimensional CR manifolds which preserve circles is either a CR diffeomorphism or a conjugate CR diffeomorphism.
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