Reference : A characterization of CR quadrics with a symmetry property
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
A characterization of CR quadrics with a symmetry property
Altomani, Andrea [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Medori, Constantino []
Journal of Geometric Analysis (The)
Springer New York LLC
Yes (verified by ORBilu)
New York
[en] CR quadric ; Homogeneous CR manifold ; Levi ; Tanaka algebra ; Involutive automorphism
[en] 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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