Finite Type Conditions on Real Hypersurfaces with One Degenerate Eigenvalue

Let M be a smooth pseudoconvex hypersurface in ℂ n +1 whose Levi form has at most one degenerate eigenvalue. For any tangent vector field L of type (1, 0), we prove the equality of the commutator type and the Levi form type associated to L . We also show that the regular contact type, the commutator type and the Levi form type of the real hypersurface are the same.