A new example of a uniformly Levi degenerate hypersurface in C3

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 Γ_C over the two-dimensional real cone in R³ is also homogeneous and has a seven-dimensional CR automorphism group. However, our example is not biholomorphic to the tube over the real cone, because the two-dimensional isotropy groups of Γ_C are, in contrast, noncommutative.