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On nondegeneracy conditions for the Levi map in higher codimension: a survey

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Abstract

We compare various definitions of nondegeneracy of the Levi map for real submanifolds of higher codimension in \({\mathbb {C}}^N\) and discuss the generalization to higher codimension of the 2-jet determination for biholomorphisms in the hypersurface case proved by Chern and Moser (Acta Math 133:219–271, 1974).

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Acknowledgements

The authors would like to thank the referee for having enriched this survey with useful references.

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Authors and Affiliations

  1. Laboratoire Paul Painlevé, Univ. Lille, CNRS, UMR 8524, 59000, Lille, France

    Léa Blanc-Centi

  2. Department of Mathematics, University of Fribourg, 1700, Perolles, Fribourg, Switzerland

    Francine Meylan

Authors
  1. Léa Blanc-Centi
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  2. Francine Meylan
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Correspondence to Léa Blanc-Centi.

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Dedicated to the memory of Nick Hanges.

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Blanc-Centi, L., Meylan, F. On nondegeneracy conditions for the Levi map in higher codimension: a survey. Complex Anal Synerg 6, 11 (2020). https://doi.org/10.1007/s40627-020-00048-7

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