Czechoslovak Mathematical Journal

, Volume 51, Issue 1, pp 139–141

The Dimension Function of Holomorphic Spaces of a Real Submanifold of an Almost Complex Manifold

  • Fernando Etayo
  • Mario Fioravanti
  • Ujue R. Trias
Article
  • 25 Downloads

Abstract

Let M be a real submanifold of an almost complex manifold \((\overline M ,\overline J )\) and let \(H_x = T_x M \cap \overline J (T_x M)\) be the maximal holomorphic subspace, for each x∈ M. We prove that c:M→ℕ,c(x)=dimHx is upper-semicontinuous.

holomorphic space submanifold almost complex 

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References

  1. [C] B.Y.Chen :Geometry of Submanifolds and its Applications.Sci.Univ. Tokyo, 1981.Google Scholar
  2. [K-N] S. Kobayashi and K. Nomizu: Foundations of Differential Geometry, II. Interscience, New York, 1969.Google Scholar
  3. [W] R. O. Wells, Jr.: Differential Analysis on Complex Manifolds. Springer, New York, 1980.Google Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2001

Authors and Affiliations

  • Fernando Etayo
    • 1
  • Mario Fioravanti
    • 1
  • Ujue R. Trias
  1. 1.Departamento de Matematicas, Estadistica y Computacion, Facultad de CienciasUniversidad de CantabriaSantanderSpain

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