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Mathematical Research Letters
Volume 29 (2022)
Number 5
Real-analytic coordinates for smooth strictly pseudoconvex CR-structures
Pages: 1461 – 1484
DOI: https://dx.doi.org/10.4310/MRL.2022.v29.n5.a7
Authors
Abstract
For a smooth strictly pseudoconvex hypersurface in a complex manifold, we give a necessary and sufficient condition for being CR-diffeomorphic to a real-analytic CR manifold. Our condition amounts to a holomorphic extension property for the canonically associated function expressing $2$-jets of the formal Segre varieties in terms of their $1$-jets. We also express this condition in equivalent terms for a Fefferman type determinant [Fe76].
Received 6 July 2020
Accepted 25 April 2021
Published 21 April 2023