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Mukai and Sakai proved that given a vector bundle$E$of rank$n$on a connected smooth projective curve of genus$g$and any$r$∈[1,$n$], there is subbundle$S$of rank$r$such that deg Hom($S, E/S$)≤$r$($n−r$)$g$. We prove a generalization of this bound for equivariant principal bundles. Our proof even simplifies the one given by Holla and Narasimhan for usual principal bundles.

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.

No abstract uploaded!

No abstract uploaded!