Commutator type and Levi type of a system of CR vector fields

Abstract

Let M be a smooth pseudoconvex real hypersurface in $C^n$ with $n\ge 2$ and let B be a subbundle of the CR tangent vector bundle of M. We prove that the commutator type and the Levi type associated with B are the same when either of them is less than 8. When the Levi type is eight or larger, we show that it is bounded from above by twice of the commutator type minus 8. Our results provide a partial solution to a generalized conjecture of D'Angelo.