NORMALIZING MAPPINGS OF AN ANALYTIC GENERIC CR MANIFOLD WITH ZERO LEVI FORM

  • Park, Won-K. (Department of Mathematics University)
  • Published : 2000.07.01

Abstract

It is well-known that an analytic generic CR submainfold M of codimension m in Cn+m is locally transformed by a biholomorphic mapping to a plane Cn$\times$Rm ⊂ Cn$\times$Cm whenever the Levi form L on M vanishes identically. We obtain such a normalizing biholomorphic mapping of M in terms of the defining function of M. Then it is verified without Frobenius theorem that M is locally foliated into complex manifolds of dimension n.

Keywords

CR submanifold;Levi form;biholomorphic mapping

References

  1. Russ. Math. Surveys, Introduction to the geometry of CR-manifolds E. M. Chirka