Abstract:

We consider the CR equivalence problem of 5-dimensional real hypersurfaces in C3 that are Levi degenerate of constant rank 1, and are 2 non-degenerate in the sense of Freeman; and we will review some of the progress made in this area. A well-known homogeneous model is the tube over the future light cone, whose Lie algebra of infinitesimal CR automorphism is isomorphic to so(2,3). In recent joint works with Zhangchi Chen, Joel Merker, and The-Anh Ta, we study such manifolds in the rigid setting, giving rise to 7-dimensional Lie sub-algebra of so(2,3), with 2 primary invariants.