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Register a new userA characterization of CR quadrics with a symmetry property
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Authors
Andrea Altomani
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We study CR quadrics satisfying a symmetry property $(tilde S)$ 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 $(tilde S)$ property in terms of their Levi-Tanaka algebras. In many cases the $(tilde S)$ 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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