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Reduction of Five-Dimensional Uniformly Levi Degenerate CR Structures to Absolute Parallelisms

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Abstract

Let \({\mathfrak{C}}_{2,1}\) be the class of connected 5-dimensional CR-hypersurfaces that are 2-nondegenerate and uniformly Levi degenerate of rank 1. We show that the CR-structures in \({\mathfrak{C}}_{2,1}\) are reducible to \({\mathfrak{so}}(3,2)\)-valued absolute parallelisms and give applications of this fact. Our result is the first instance of reduction to absolute parallelisms for Levi degenerate CR-structures.

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Acknowledgements

We are grateful to A. Čap for many useful conversations. The second author would like to thank the Australian National University for its hospitality during his visit to Canberra in 2012 when this work was initiated.

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Authors and Affiliations

  1. Department of Mathematics, The Australian National University, Canberra, ACT, 0200, Australia

    Alexander Isaev

  2. School of Mathematics, Trinity College Dublin, Dublin 2, Ireland

    Dmitri Zaitsev

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  1. Alexander Isaev
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  2. Dmitri Zaitsev
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Correspondence to Alexander Isaev.

Additional information

A. Isaev was supported by the Australian Research Council.

D. Zaitsev was supported in part by Science Foundation Ireland grant 10/RFP/MTH2878.

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Isaev, A., Zaitsev, D. Reduction of Five-Dimensional Uniformly Levi Degenerate CR Structures to Absolute Parallelisms. J Geom Anal 23, 1571–1605 (2013). https://doi.org/10.1007/s12220-013-9419-4

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  • DOI: https://doi.org/10.1007/s12220-013-9419-4

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