Elliptic CR-manifolds and shear invariant ODE with additional symmetries

Details Elliptic CR-manifolds and shear invariant ODE with additional symmetries Elliptic CR-manifolds and shear invariant ODE with additional symmetries

2005-09-07

arxiv.org/abs/math/0509173v1

Mathematics

Complex Variables

Scientific paper

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.

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