Skip to main content
SpringerLink
Log in

Hypersurfaces through higher-codimensional submanifolds of ℂn with preserved Levi-kernelwith preserved Levi-kernel

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

For a “generic” submanifoldS of a complex manifoldX, we show that there exists a hypersurfaceM⊃S which has the same number of negative (or positive) Levi-eigenvalues asS at one prescribed conormal (cf. also [9]). When ranksL S is constant, thenM may be found such thatL M andL S have the same number of negative eigenvalues at any common conormal. Assuming the existence of a hypersurfaceM with the above property, we then discuss the link between complex submanifolds ofS whose tangent plane belongs to the null-space of the Levi-formL S ofS (of all complex submanifolds whenL S is semi-definite), and complex submanifolds ofT * S X. As an application we give a simple result on propagation of microanalyticity for CR-hyperfunctions along complex,L S -null, curves (cf. [3]).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Bedford and J. E. Fornaess,Complex manifolds in pseudoconvex boundaries, Duke Mathematical Journal48 (1981), 279–287.

    Article  MATH  MathSciNet  Google Scholar 

  2. A. D’Agnolo and G. Zampieri,Microlocal direct images of simple sheaves with applications to systems with simple characteristics, Bulletin de la Société Mathématique de France23 (1995), 101–133.

    Google Scholar 

  3. N. Hanges and F. Treves,Propagation of holomorphic extendability of CR functions, Mathematische Annalen263 (1983), 157–177.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Kashiwara and P. Schapira,Microlocal theory of sheaves, Astérisque128 (1985).

  5. J.-M. Trépreau,Sur la propagation des singularités dans les varietés CR, Bulletin de la Société Mathématique de France118 (1990), 129–140.

    Google Scholar 

  6. J.-M. Trépreau,Systèmes différentiels à caractéristiques simples et structures réelles-complexes (d'après Baouendi-Trèves et Sato-Kashiwara-Kawai), Séminaire Bourbaki595 (1981–82).

  7. A. Tumanov,Connections and propagation of analyticity for CR functions, Duke Mathematical Journal73 (1994), 1–24.

    Article  MATH  MathSciNet  Google Scholar 

  8. A. Tumanov,On the propagation of extendibility of CR functions, inComplex Analysis and Geometry, Lecture Notes in Pure and Applied Mathematics, Marcel-Dekker, 1995, pp. 479–498.

  9. G. Zampieri, Extension of submanifolds of ℂn preserving the number of negative eigenvalues, Preprint, 1995.

  10. G. Zampieri, The Andreotti-Grauert vanishing theorem for dihedrons of ℂn, Journal of Mathematical Sciences of the University of Tokyo2 (1995), 233–246.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università, v. Belzoni 7, 35131, Padova, Italy

    Giuseppe Zampieri

Authors
  1. Giuseppe Zampieri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giuseppe Zampieri.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zampieri, G. Hypersurfaces through higher-codimensional submanifolds of ℂn with preserved Levi-kernelwith preserved Levi-kernel. Isr. J. Math. 101, 179–188 (1997). https://doi.org/10.1007/BF02760928

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02760928

Keywords

Search

Navigation