Normal forms and biholomorphic equivalence of real hypersurfaces in C^3

Details Normal forms and biholomorphic equivalence of real hypersurfaces in C^3 Normal forms and biholomorphic equivalence of real hypersurfaces in C^3

1997-05-29

arxiv.org/abs/math/9705201v1

Mathematics

Complex Variables

Scientific paper

We consider the problem of describing the local biholomorphic equivalence class of a real-analytic hypersurface $M$ at a distinguished point $p_0\in M$ by giving a normal form for such objects. In order for the normal form to carry useful information about the biholomorphic equivalence class, we shall require that the transformation to normal form is unique modulo some finite dimensional group. A classical result due to Chern--Moser gives such a normal form for Levi nondegenerate hypersurfaces. The main results in this paper concern real-analytic hypersurfaces $M$ in $\Bbb C^3$ at certain Levi degenerate points $p_0\in M$, namely points at which $M$ is 2-nondegenerate. We give a partial normal form for all such $(M,p_0)$, i.e. a normal form for the data associated with 2-nondegeneracy. We also give a complete formal normal form for such $(M,p_0)$ under the additional condition that the Levi form has rank one at $p_0$. This result, combined with a recent theorem due to the author, M. S. Baouendi, and L. P. Rothschild stating that formal equivalences between real-analytic finitely nondegenerate hypersurfaces converge, gives a description of the biholomorphic equivalence class of a real-analytic hypersurface in $\Bbb C^3$ at a point of 2-nondegeneracy where the rank of the Levi form is one.

Affiliated with

Also associated with

No associations

Rating

Normal forms and biholomorphic equivalence of real hypersurfaces in C^3 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Normal forms and biholomorphic equivalence of real hypersurfaces in C^3, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Normal forms and biholomorphic equivalence of real hypersurfaces in C^3 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-329901