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Inflexible CR submanifolds

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Abstract

In this paper we introduce the concept of inflexible CR submanifolds. These are CR submanifolds of some complex Euclidean space such that any compactly supported CR deformation is again globally CR embeddable into some complex Euclidean space. Our main result is that any 2-pseudoconcave quadratic CR submanifold of type (n, d) in \(\mathbb {C}^{n+d}\) is inflexible.

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Acknowledgements

The first author was supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Grant BR 3363/2-1).

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Authors and Affiliations

  1. Mathematisches Institut, Universität Leipzig, Augustusplatz 10, D-04109, Leipzig, Germany

    Judith Brinkschulte

  2. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794, USA

    C. Denson Hill

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  1. Judith Brinkschulte
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  2. C. Denson Hill
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Correspondence to Judith Brinkschulte.

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Brinkschulte, J., Hill, C.D. Inflexible CR submanifolds. Math. Z. 287, 461–472 (2017). https://doi.org/10.1007/s00209-016-1831-6

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  • DOI: https://doi.org/10.1007/s00209-016-1831-6

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