New invariant tensors in CR structures and a normal form for real hypersurfaces at a generic Levi degeneracy
Abstract
Description
We introduce new invariant tensors in CR structures which can be viewed as higher order Levi forms. Using the second and third order tensors, we give a complete formal normal form (in the sense of Chern-Moser) for a real hypersurface at a generic Levi degeneracy. (We say that M has a generic Levi degeneracy at p if the Levi determinant vanishes at p but its differential does not, and the set of Levi degenerate points of M is transverse to the Levi null space at p.) By applying a convergence theorem for formal mappings due to the author, Baouendi, and Rothschild, we conclude that the above mentioned formal normal form provides a complete set of biholomorphic invariants for real-analytic hypersurfaces at generic Levi degeneracies.
31 pages, AMS-TeX format; the normal form has been extended to the indefinite case
31 pages, AMS-TeX format; the normal form has been extended to the indefinite case