Skip to main content
SpringerLink
Log in

Total curvatures of compact complex submanifolds in\(C/P^n\)

  • Published:
Annals of Global Analysis and Geometry Aims and scope Submit manuscript

Abstract

LetM be a complex submanifold in\(C/P^n\). We define the total curvatures ofM and we get a local interpretation of them. Finally, we give a topological characterization for the total (non-absolute) curvature of complex hypersurfaces in\(C/P^n\).

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. Chern, S.S.:Complex Manifolds Without Potential Theory. Springer-Verlag, New York 1979.

    Google Scholar 

  2. Chern, S.S.;Griffiths, P.: Abel's Theorem and Webs.Jahresber. Dtsch. Math.-Ver. 80 (1978), 13–110.

    Google Scholar 

  3. Chern, S.S.;Lashof, K.: On the total curvature of immersed manifolds.Am. J. Math. 79 (1957), 246–258.

    Google Scholar 

  4. Flaherty, F.J.: The volume of a tube in complex projective space.Ill. J. Math. 16 (1972), 627–638.

    Google Scholar 

  5. Griffiths, P.A.: Complex differential and integral geometry and curvature integrals associated to singularities of complex analytic varieties.Duke Math. J. 45 (1978), 427–512.

    Google Scholar 

  6. Gray, A.:Tubes. Addison Wesley Publishing Company, Inc., 1990.

  7. Gual, X.: Measure of linear spaces and total curvatures of compact anti-invariant submanifolds in\(C/^n\).Proc. Conf. Differential Geometry and Applications, Opava (1992), pp. 13–22.

  8. Ishihara, T.: Some Integral Formulas in Complex Projective Spaces.J. Math., Tokushima Univ. 17 (1983), 15–20.

    Google Scholar 

  9. Ishihara, T.: Total curvatures of Kaehler manifolds in complex projective spaces.Geom. Dedicata 20 (1986), 307–318.

    Google Scholar 

  10. Santaló, L.A.: Curvaturas absolutas totales de variedades contenidas en un espacio euclidiano.Acta Cient. Compostelana 5 (1969), 149–158.

    Google Scholar 

  11. Santaló, L.A.: Mean values and curvatures.Izv. Akad. Nauk. Armjan SSR Sr. Mat. 5 (1970), 286–295.

    Google Scholar 

  12. Santaló, L.A.: Total curvatures of compact manifolfds immersed in euclidean space.Simp. Mat. Ist. Naz. Alta Mat. Roma 14 (1974), 364–390.

    Google Scholar 

  13. Santaló, L.A.: Integral geometry in Hermitian spaces.Am. J. Math. 74 (1952). 423–434.

    Google Scholar 

  14. Santaló, L.A.:Integral Geometry and Geometric Probability. Addison Wesley Publishing Company, Inc, London 1976.

    Google Scholar 

  15. Shifrin, T.: The kinematic formula in complex integral geometry.Trans. Am. Math. Soc. 264 (1981), 255–293.

    Google Scholar 

  16. Weyl, H.: On the volume of tubes.Amer. J. Math. 61 (1939), 461–472.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. de Matemàtiques, Universitat Jaume I Campus Penyeta Roja, 12071, Castelló, Spain

    Ximo Gual Arnau

  2. Dpto. de Geometría y Topología, Universitat de València, C/Dr. Moliner 50, 46100, Burjasot (València), Spain

    Antonio M. Naveira

Authors
  1. Ximo Gual Arnau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonio M. Naveira
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by Fundació Caixa Castelló grant n. MI25043/92.

Partially supported by the Spanish DGICYT grant #PB91 — 0324.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Arnau, X.G., Naveira, A.M. Total curvatures of compact complex submanifolds in\(C/P^n\) . Ann Glob Anal Geom 13, 9–18 (1995). https://doi.org/10.1007/BF00774562

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00774562

Key words

MSC 1991

Search

Navigation