Real-analytic coordinates for smooth strictly pseudoconvex CR-structures

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Authors

KOSSOVSKIJ Ilja ZAITSEV Dmitri

Year of publication 2022
Type Article in Periodical
Magazine / Source Mathematical Research Letters
MU Faculty or unit

Faculty of Science

Citation
Web
Doi http://dx.doi.org/10.4310/MRL.2022.v29.n5.a7
Keywords strictly pseudoconvex hypersurfaces; CR-mappings; CR-structures; analytic regularity; change of complex structure; leaf space of foliation
Description 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].
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