Abstract
We present a homogeneous real analytic hypersurface in C3, two-nondegenerate, uniformly Levi degenerate of rank one, with a seven-dimensional CR automorphism group such that the isotropy group of each point is two-dimensional and commutative. The classical tube ΓC over the two-dimensional real cone in R3 is also homogeneous and has a seven-dimensional CR automorphism group. However, our example isnot biholomorphic to the tube over the real cone, because the two-dimensional isotropy groups of ΓC are, in contrast, noncommutative.
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