Levi flat hypersurfaces which are not holomorphically flat

Bedford, Eric; De Bartolomeis, Paolo

doi:10.1090/S0002-9939-1981-0601733-2

Levi flat hypersurfaces which are not holomorphically flat
HTML articles powered by AMS MathViewer

by Eric Bedford and Paolo De Bartolomeis PDF

Proc. Amer. Math. Soc. 81 (1981), 575-578 Request permission

Abstract:

A real analytic, Levi flat hypersurface $S \subset {{\mathbf {C}}^n}$ is locally biholomorphically flat. It is shown here that if $S$ is Levi flat and ${C^\infty }$, then in general it is not possible to flatten $S$, even in a local, "one-sided" sense.

References

S. S. Chern and J. K. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219–271. MR 425155, DOI 10.1007/BF02392146
James J. Faran V, Non-analytic hypersurfaces in $\textbf {C}^{n}$, Math. Ann. 226 (1977), no. 2, 121–123. MR 430295, DOI 10.1007/BF01360863
Charles Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65. MR 350069, DOI 10.1007/BF01406845
G. M. Henkin, An analytic polyhedron is not holomorphically equivalent to a strictly pseudoconvex domain, Dokl. Akad. Nauk SSSR 210 (1973), 1026–1029 (Russian). MR 0328125
S. I. Pinčuk, Biholomorphic inequivalence of bounded domains with smooth and piecewise-smooth boundaries, Dokl. Akad. Nauk SSSR 247 (1979), no. 3, 554–557 (Russian). MR 545691
C. Rea, Levi-flat submanifolds and holomorphic extension of foliations, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 26 (1972), 665–681. MR 425158