manuscripta mathematica

, Volume 59, Issue 3, pp 261–276 | Cite as

An extension of Calabi's rigidity theorem to complex submanifolds of indefinite complex space forms

  • Alfonso Romero


The rigidity for full holomorphic isometric immersions of an indefinite Kähler manifold into an indefinite complex space form is proved. All such immersions between indefinite complex projective (and hyperbolic) spaces are founded and examples of non-congruents holomorphic isometric immersions are exposed.


Number Theory Algebraic Geometry Topological Group Complex Space Space Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Barros, A. Romero, “Indefinite Kähler manifolds”, Math. Ann.261, 55–62 (1982)Google Scholar
  2. [2]
    S. Bochner, “Curvature in Hermitian metric”, Bull. Amer. Math. Soc.53, 179–195 (1947)Google Scholar
  3. [3]
    E. Calabi, “Isometric imbeddings of complex manifolds”, Ann. of Math.58, 1–23 (1953)Google Scholar
  4. [4]
    S. Montiel, A. Romero, “Complex Einstein hypersurfaces of indefinite complex space forms”, Math. Proc. Camb. Phil. Soc.94 495–508 (1983)Google Scholar
  5. [5]
    K. Nomizu, B. Smyth, “Differential geometry of complex hypersurfaces II”, J. Math. Soc. Japan20, 498–521 (1968)Google Scholar
  6. [6]
    A. Romero, “Some examples of complete indefinite complex Einstein hypersurfaces not locally symmetric”, Proc. Amer. Math. Soc.98, 283–286 (1986)Google Scholar
  7. [7]
    A. Romero, “On a certain class of complex Einstein hypersurfaces in indefinite complex space forms”, Math. Zeitschrift192, 627–635 (1986)Google Scholar
  8. [8]
    J. A. Wolf, Spaces of constant curvature, McGraw-Hill, 1967Google Scholar
  9. [9]
    H. Wu, “The Bochner technique”, Proc. of the 1980 Beijing Symposium on Differential Geometry and Differential Equations, Science Press, Beijing, People's Republic of China, Vol 2 929–1071 (1982)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Alfonso Romero
    • 1
  1. 1.Departamento de Geometría y TopologíaUniversidad de GranadaGranadaSpain

Personalised recommendations