Projective classification of lines and quadric sections in Q^{2,2} produces a one-parameter family of real-analytic non-spherical Levi-nondegenerate CR structures on S^3 parameterized by Coxeter's inversive distance.
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The Flat CR Twistor Model $Q^{2,2}$ and Its Algebraic Sections
Projective classification of lines and quadric sections in Q^{2,2} produces a one-parameter family of real-analytic non-spherical Levi-nondegenerate CR structures on S^3 parameterized by Coxeter's inversive distance.