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Elliptic CR-manifolds and shear invariant ODE with additional symmetries

Vladimir Ezhov·Gerd Schmalz
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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.

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Vladimir Ezhov, Gerd Schmalz. 2005-09-07. Elliptic CR-manifolds and shear invariant ODE with additional symmetries. https://doi.org/10.1007/s11512-007-0049-6

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