q-pseudoconvex hypersurfaces through higher codimensional submanifolds of C-N

摘要

We give a criterion for "extending" a higher codimensional real submanifold of C-N to a hypersurface preserving the number of negative Levi-eigenvalues. Precisely, if S is a real analytic generic submanifold of C-N with "microlocally" constant Levi-rank, then there exists a real analytic hypersurface M superset of S with the same number of negative eigenvalues as S and still of constant rank. A partial result of this type was already stated in [10] but only for the common conormals to M and S. This criterion of "extending" manifolds has useful applications as for instance to non-solvability of the tangential (&PARTIAL;) over bar system. [References: 12]