Riv. Mat. Univ. Parma, Vol. 13, No. 2, 2022
Stefano Marini ^{[a]}
On finitely Levi non degenerate homogeneous \(CR\) manifolds
Pages: 353372
Received: 26 November 2021
Accepted in revised form: 22 April 2022
Mathematics Subject Classification: Primary: 32V35, 32V40, Secondary: 17B22, 17B10.
Keywords: Lie pair, \(CR\) algebra, Lie algebra extension, Levi degeneracy.
Author address:
[a]: Università di Parma, Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Parma, Italy
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Abstract:
A \(CR\) manifold M is a differentiable manifold together with a complex
subbundle of the complexification of its tangent bundle, which is formally
integrable and has zero intersection with its conjugate bundle. A fundamental
invariant of a \(CR\) manifold \(\textsf{M}\)
is its vectorvalued Levi form. A Levi non degenerate \(CR\) manifold of order \(k \geq 1\) has
non degenerate Levi form in a higher order sense. For a (locally) homogeneous
manifold Levi non degeneracy of order \(k\) can be described in terms of its \(CR\) algebra,
i.e. a pair of Lie algebras encoding the structure of (locally) homogeneous \(CR\) manifolds.
I will give an introduction to these topics presenting some recent results.
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