Mathematical Research Letters

Volume 29 (2022)

Number 5

Real-analytic coordinates for smooth strictly pseudoconvex CR-structures

Pages: 1461 – 1484



I. Kossovskiy (Department of Mathematics, Masaryk University, Brno, Czech Republic; and Faculty of Mathematics, University of Vienna, Austria)

D. Zaitsev (School of Mathematics, Trinity College Dublin, Ireland)


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