Skip to main content
SpringerLink
Log in

Cartan-Fubini Type Extension Theorems

  • Published:
Acta Mathematica Vietnamica Aims and scope Submit manuscript

Abstract

Liouville’s theorem in conformal geometry can be generalized to extension problems of holomorphic maps preserving certain structures on Fano manifolds. The most typical result of this type is Cartan-Fubini type extension theorem proved by Mok and myself. We give an introduction to this circle of problems and survey some recent results.

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. Blair, D.E.: Inversion theory and conformal mapping. Student Math. Library 9 A.M.S (2000)

  2. Cartan, E.: Sur la déformation projective des surfaces. Ann. Sci. Ecole Norm. Sup. 37, 259–356 (1920)

    MathSciNet  MATH  Google Scholar 

  3. Fubini, G.: Sudi relativi all’ellemento lineare proiettivo di una ipersuperficie. Rend. Acad. nz. dei Lincei, 99–106 (1918)

  4. Hwang, J.-M.: Deformation of holomorphic maps onto the blow-up of the projective plane. Ann. Sci. Ecole Norm. Sup. 40, 179–189 (2007)

    MathSciNet  MATH  Google Scholar 

  5. Hwang, J.-M.: Webs of algebraic curves preprint (2015)

  6. Hwang, J.-M., Mok, N.: Cartan-fubini type extension of holomorphic maps for Fano manifolds of Picard number 1. Journal Math. Pures Appl. 80, 563–575 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jensen, G., Musso, E.: Rigidity of hypersurfaces in complex projective space. Ann. Sci. Ecole Norm. Sup. 27, 227–248 (1994)

    MathSciNet  MATH  Google Scholar 

  8. Kobayashi, S., Nagano, T.: On filtered Lie algebras and geometric structures 1. J. Math. Mech. 13, 875–908 (1964)

    MathSciNet  MATH  Google Scholar 

  9. Sasaki, T.: Projective differential geometry and linear homogeneous differential equations (Notes of Lectures at Brown Univ. 1988/89). Rokko Lectures in Mathematics 5 (1999)

  10. Tanaka, N.: On the equivalence problems associated with simple graded Lie algebras. Hokkaido. Math. H 8, 23–84 (1979)

    MATH  Google Scholar 

  11. Yamaguchi, K.: Differential systems associated with simple graded Lie algebras. Adv. Study Pure Math. 22, 413–494 (1993)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Korea Institute for Advanced Study, Hoegiro 87, Seoul, 130-722, Korea

    Jun-Muk Hwang

Authors
  1. Jun-Muk Hwang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jun-Muk Hwang.

Additional information

Lecture at the Annual Meeting 2015 of the Vietnam Institute for Advanced Study in Mathematics

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hwang, JM. Cartan-Fubini Type Extension Theorems. Acta Math Vietnam 41, 369–377 (2016). https://doi.org/10.1007/s40306-016-0173-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40306-016-0173-0

Keywords

Mathematics Subject Classification (2010)

Search

Navigation