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Locally homogeneous finitely nondegenerate CR-manifolds

Gregor Fels
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Abstract

Germs of locally homogeneous CR manifolds M can be characterized in terms of certain algebraic data, e.g., by CR-algebras. We give an explicit formula which relates the Levi form of such an M and its higher order analogues to the Lie brackets in certain finite dimensional Lie algebras. As an application we give a simple characterization of geometric properties of M such as minimality, k-nondegeneracy, holomorphic degeneracy etc. in purely algebraic terms. We present an example of a homogeneous 3-nondegenerate CR-manifold. We also determine a universal upper bound for the order k of k-nondegenerate orbits of real forms in flag manifolds.

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Gregor Fels. 2006-06-01. Locally homogeneous finitely nondegenerate CR-manifolds. https://arxiv.org/abs/math/0606032

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