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Diffeomorphisms preserving R‐circles in three dimensional CR manifolds |
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| Authors: | E Falbel J M Veloso |
| Institution: | 1. Sorbonne Universités‐UPMC, Institut de Mathématiques de Jussieu‐Paris Rive Gauche F‐75005, Paris, France;2. INRIA Paris‐Rocquencourt Research Center, Paris, France;3. Faculdade de Matemática – ICEN Universidade Federal do Pará, Belém, PA, Brazil |
| Abstract: | R ‐circles in (non‐degenerate) three dimensional CR manifolds are the analogues to traces of Lagrangian totally geodesic planes on S3 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. |
| Keywords: | CR structures R‐circles Cartan connection 58A15 53C17 53D10 32V05 |