Diffeomorphisms preserving R-circles in three dimensional CR manifolds

2013/07/29 by Elisha Falbel, Falbel, E., José M. M. Veloso +1
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1307.7636

openalex publication_date 2013/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

R-circles in general three dimensional CR manifolds (of contact type) are the analogues to traces of Lagrangian totally geodesic planes on the sphere 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 conjugate CR diffeomorphism.

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