# Higher order Levi forms on homogeneous CR manifolds

@article{Marini2020HigherOL, title={Higher order Levi forms on homogeneous CR manifolds}, author={Stefano Marini and Costantino Medori and Mauro Nacinovich}, journal={Mathematische Zeitschrift}, year={2020}, volume={299}, 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.

## 4 Citations

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We investigate 3-nondegenerate CR structures in the lowest possible dimension 7, and one of our goals is to prove Beloshapka's conjecture on the symmetry dimension bound for hypersurfaces in $C^4$.…

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. In this paper we show that two K¨ahler manifolds which do not share a K¨ahler submanifold, do not share either a Levi degenerate CR–submanifold with constant dimension Levi kernel. In particular,…

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A bstract . A complex ﬂag manifold F = G / Q decomposes into ﬁnitely many real orbits under the action of a real form G σ of G . Their embedding into F deﬁne on them CR manifold structures. We…

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