Czechoslovak Mathematical Journal

, Volume 64, Issue 1, pp 79–90 | Cite as

Ideal CR submanifolds in non-flat complex space forms

  • Toru Sasahara


An explicit representation for ideal CR submanifolds of a complex hyperbolic space has been derived in T. Sasahara (2002). We simplify and reformulate the representation in terms of certain Kähler submanifolds. In addition, we investigate the almost contact metric structure of ideal CR submanifolds in a complex hyperbolic space. Moreover, we obtain a codimension reduction theorem for ideal CR submanifolds in a complex projective space.


δ-invariants CR submanifolds ideal submanifolds 

MSC 2010

53C42 53B25 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. Y. Chen: CR-submanifolds of a Kähler manifold. I. J. Differ. Geom. 16 (1981), 305–322.MATHGoogle Scholar
  2. [2]
    B. Y. Chen: CR-submanifolds of a Kähler manifold. II. J. Differ. Geom. 16 (1981), 493–509.MATHGoogle Scholar
  3. [3]
    B. Y. Chen: Some new obstructions to minimal and Lagrangian isometric immersions. Jap. J. Math., New Ser. 26 (2000), 105–127.MATHGoogle Scholar
  4. [4]
    B. Y. Chen: Pseudo-Riemannian Geometry, δ-Invariants and Applications. World Scientific, Hackensack, NJ, 2011.CrossRefGoogle Scholar
  5. [5]
    B. Y. Chen, G. D. Ludden, S. Montiel: Real submanifolds of a Kähler manifold. Algebras Groups Geom. 1 (1984), 176–212.MATHMathSciNetGoogle Scholar
  6. [6]
    M. Djorić, M. Okumura: CR Submanifolds of Complex Projective Space. Developments in Mathematics 19. Springer, Berlin, 2010.CrossRefMATHGoogle Scholar
  7. [7]
    M. Okumura: Codimension reduction problem for real submanifolds of complex projective space. Differential Geometry and Its Applications (Eger, 1989). Colloq. Math. Soc. János Bolyai 56. North-Holland, Amsterdam, 1992, pp. 573–585.Google Scholar
  8. [8]
    T. Sasahara: On Ricci curvature of CR-submanifolds wit rank one totally real distribution. Nihonkai Math. J. 12 (2001), 47–58.MATHMathSciNetGoogle Scholar
  9. [9]
    T. Sasahara: On Chen invariant of CR-submanifolds in a complex hyperbolic space. Tsukuba J. Math. 26 (2002), 119–132.MATHMathSciNetGoogle Scholar

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2014

Authors and Affiliations

  1. 1.Division of Mathematics, Center for Liberal Arts and SciencesHachinohe Institute of TechnologyHachinohe AomoriJapan

Personalised recommendations