English

Elliptic CR-manifolds and shear invariant ODE with additional symmetries

Complex Variables 2015-02-13 v1 Classical Analysis and ODEs

Abstract

We classify the ODEs that correspond to elliptic CR-manifolds with maximal isotropy. It follows that the dimension of the isotropy group of an elliptic CR-manifold can be only 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 istropy group, except for two special manifolds, the points with non-linearizable isotropy form exactly some complex curve on the manifold.

Keywords

Cite

@article{arxiv.math/0509173,
  title  = {Elliptic CR-manifolds and shear invariant ODE with additional symmetries},
  author = {Vladimir Ezhov and Gerd Schmalz},
  journal= {arXiv preprint arXiv:math/0509173},
  year   = {2015}
}