Higher order Levi forms on homogeneous CR manifolds

  title={Higher order Levi forms on homogeneous CR manifolds},
  author={Stefano Marini and Costantino Medori and Mauro Nacinovich},
  journal={Mathematische Zeitschrift},
  pages={563 - 589}
We investigate the nondegeneracy of higher order Levi forms on weakly nondegenerate homogeneous CR manifolds. Improving previous results, we prove that general orbits of real forms in complex flag manifolds have order less or equal than 3 and the compact ones less or equal 2. Finally we construct by Lie extensions weakly nondegenerate CR vector bundles with arbitrary orders of nondegeneracy. 
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