CR-quadrics with a symmetry property

Kaup, Wilhelm

doi:10.1007/s00229-010-0383-z

Cited by 2 publications

(4 citation statements)

References 9 publications

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“…Definition 3.4. The quadricQ =Q H associated to H is the standard CR manifold S(g) associated to g. This definition agrees with the definition in [8] (see also [7]).…”

Section: Cr Quadricssupporting

confidence: 69%

“…In [8] W. Kaup introduced a symmetry property, called property (S), for the quadric Q. Here we consider the following generalization.…”

Section: Cr Quadricsmentioning

confidence: 99%

“…In [8] W. Kaup defined a quadric Q to have the symmetry property (S) if there is an involutive CR automorphism γ of Q such that Ad(γ)(g j ) = g −j for j = 0, ±1, ±2.…”

Section: Introductionmentioning

confidence: 99%

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A Characterization of CR Quadrics with a Symmetry Property

Altomani

Medori

2011

J Geom Anal

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We study CR quadrics satisfying a symmetry property (S) which is slightly weaker than the symmetry property (S), recently introduced by W. Kaup, which requires the existence of an automorphism reversing the gradation of the Lie algebra of infinitesimal automorphisms of the quadric.We characterize quadrics satisfying the (S) property in terms of their Levi-Tanaka algebras. In many cases the (S) property implies the (S) property; this holds in particular for compact quadrics.We also give a new example of a quadric such that the dimension of the algebra of positive-degree infinitesimal automorphisms is larger than the dimension of the quadric.

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“…Definition 3.4. The quadricQ =Q H associated to H is the standard CR manifold S(g) associated to g. This definition agrees with the definition in [8] (see also [7]).…”

Section: Cr Quadricssupporting

confidence: 69%

“…In [8] W. Kaup introduced a symmetry property, called property (S), for the quadric Q. Here we consider the following generalization.…”

Section: Cr Quadricsmentioning

confidence: 99%

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A Characterization of CR Quadrics with a Symmetry Property

Altomani

Medori

2011

J Geom Anal

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“…Furthermore, a dense open subset of S can be realized as a real quadric in C m(n−m) , and g := su( p, q) = hol(S) ∼ = hol(S, a) holds for every a ∈ S, cf. [17] for details. As a consequence of Theorem 1.3 in [15], cf.…”

Section: Classification Of Involutions For Certain Cr-manifoldsmentioning

confidence: 99%

Local tube realizations of CR-manifolds and maximal abelian subalgebras

Fels¹,

Kaup²

2011

Annali Scuola Normale Superiore - Classe Di Scienze

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For every real-analytic CR-manifold M we give necessary and sufficient conditions that M can be realized in a suitable neighbourhood of a given point a ∈ M as a tube submanifold of some C r . We clarify the question of the 'right' equivalence between two local tube realizations of the CR-manifold germ (M, a) by introducing two different notions of affine equivalence. One of our key results is a procedure that reduces the classification of equivalence classes to a purely algebraic manipulation in terms of Lie theory.

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CR-quadrics with a symmetry property

Cited by 2 publications

References 9 publications

A Characterization of CR Quadrics with a Symmetry Property

A Characterization of CR Quadrics with a Symmetry Property

Local tube realizations of CR-manifolds and maximal abelian subalgebras

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