CR Embeddings, Chains, and the Fefferman Bundle

2010/10/17 by André Minor, Minor, André
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #math.DG

paper · pdf · doi:10.48550/arxiv.1010.3458

openalex publication_date 2010/10/17 · arxiv created 2013/03/12 · arxiv updated 2013/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper it is shown that a CR embedding from one strictly pseudoconvex hypersurface into another (of strictly larger dimension) sends chains on the source to chains on the target if and only if the embedding has a lift to a conformal isometry of the associated Fefferman bundles with vanishing pseudo-Riemannian second fundamental form. When the target is a sphere these conditions simplify nicely.

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