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Elliptic CR-manifolds and shear invariant ordinary differential equations with additional symmetries

Vladimir Ezhov School of Mathematics and Statistics, University of South Australia Gerd Schmalz School of Mathematics, Statistics and Computer Science, University of New England

TBD mathscidoc:1701.333113

Arkiv for Matematik, 45, (2), 253-268, 2005.12
We classify the ordinary differential equations that correspond to elliptic CR-manifolds with maximal isotropy. It follows that the dimension of the isotropy group of an elliptic CR-manifold can only be 10 (for the quadric), 4 (for the listed examples) or less. This is in contrast with the situation of hyperbolic CR-manifolds, where the dimension can be 10 (for the quadric), 6 or 5 (for semi-quadrics) or less than 4. We also prove that, for all elliptic CR-manifolds with non-linearizable isotropy group, except for two special manifolds, the points with non-linearizable isotropy form exactly some complex curve on the manifold.
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@inproceedings{vladimir2005elliptic,
  title={Elliptic CR-manifolds and shear invariant ordinary differential equations with additional symmetries},
  author={Vladimir Ezhov, and Gerd Schmalz},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203620757644922},
  booktitle={Arkiv for Matematik},
  volume={45},
  number={2},
  pages={253-268},
  year={2005},
}
Vladimir Ezhov, and Gerd Schmalz. Elliptic CR-manifolds and shear invariant ordinary differential equations with additional symmetries. 2005. Vol. 45. In Arkiv for Matematik. pp.253-268. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203620757644922.
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