A characterization of CR quadrics with a symmetry property

Details A characterization of CR quadrics with a symmetry property A characterization of CR quadrics with a symmetry property

2010-11-15

arxiv.org/abs/1011.3358v2

Mathematics

Complex Variables

16 pages. v2: minor revision, added references

Scientific paper

10.1007/s12220-011-9228-6

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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