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A new example of a uniformly Levi degenerate hypersurface in C^{3}

Hervé Gaussier Centre de Mathématiques et Informatique, Université de Provence Joël Merker Centre de Mathématiques et Informatique, Université de Provence

TBD mathscidoc:1701.332994

Arkiv for Matematik, 41, (1), 85-94, 2001.11
We present a homogeneous real analytic hypersurface in C^{3}, two-nondegenerate, uniformly Levi degenerate of rank one, with a seven-dimensional CR automorphism group such that the isotropy group of each point is two-dimensional and commutative. The classical tube Γ_{C}over the two-dimensional real cone in R^{3}is also homogeneous and has a seven-dimensional CR automorphism group. However, our example is$not$biholomorphic to the tube over the real cone, because the two-dimensional isotropy groups of Γ_{C}are, in contrast, noncommutative.
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@inproceedings{hervé2001a,
  title={A new example of a uniformly Levi degenerate hypersurface in C^{3}},
  author={Hervé Gaussier, and Joël Merker},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203606083160803},
  booktitle={Arkiv for Matematik},
  volume={41},
  number={1},
  pages={85-94},
  year={2001},
}
Hervé Gaussier, and Joël Merker. A new example of a uniformly Levi degenerate hypersurface in C^{3}. 2001. Vol. 41. In Arkiv for Matematik. pp.85-94. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203606083160803.
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