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
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by Eric Bedford and Paolo De Bartolomeis

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

DOI: https://doi.org/10.1090/S0002-9939-1981-0601733-2

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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.

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