Ukrainian Mathematical Journal

, Volume 62, Issue 11, pp 1803–1809 | Cite as

A note on invariant submanifolds of (k, μ)-contact manifolds

Brief Communications

The object of the present paper is to study invariant submanifolds of a (k, μ)-contact manifold and to find the necessary and sufficient conditions for an invariant submanifold of a (k, μ)-contact manifold to be totally geodesic.


Riemannian Manifold Fundamental Form Contact Structure Riemannian Space Isometric Immersion 
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.
    D. E. Blair, “Two remarks on contact metric structure,” Tohoku Math J., 29, 319–324 (1977).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    D. E. Blair, “Riemannian geometry of contact and symplectic manifolds,” Progr. Math., 203 (1979).Google Scholar
  3. 3.
    D. E. Blair, T. Koufogiorgos, and B. J. Papantoniou, “Contact metric manifolds satisfying a nullity condition,” Isr. J. Math., 91, 189–214 (1995).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    E. Boeckx, “A full classification of contact metric (k, μ)-spaces,” Ill. J. Math., 44, 212–219 (2000).MathSciNetzbMATHGoogle Scholar
  5. 5.
    E. Boeckx, “A class of locally ϕ-symmetric contact metric spaces,” Arch. Math. (Basel), 72, 466–472 (1999).MathSciNetzbMATHGoogle Scholar
  6. 6.
    E. Boeckx, “Contact-homogeneous locally ϕ-symmetric manifolds,” Glasgow Math. J., 48, 93–109 (2006).MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    B. Y. Chen, “Geometry of submanifolds,” Pure Appl. Math., No. 22 (1973).Google Scholar
  8. 8.
    J. Deprez, “Semiparallel surfaces in the Euclidean space,” J. Geom., 25, 192–200 (1985).MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    J. Deprez, “Semiparallel hypersurfaces,” Rend. Semin. Mat. Univ. Politecn. Torino, 44, 303–316 (1986).MathSciNetzbMATHGoogle Scholar
  10. 10.
    Endo H., “Certain submanifolds of contact metric manifolds,” Tensor (N. S.), 47, No. 2, 198–202 (1988).MathSciNetzbMATHGoogle Scholar
  11. 11.
    M. Kon, “Invariant submanifolds of normal contact metric manifolds,” Kodai Math. Sem. Rep., 27, 330–336 (1973).MathSciNetCrossRefGoogle Scholar
  12. 12.
    U. Lumiste, “Semisymmetric submanifolds as the second-order envelope of symmetric submanifolds,” Proc. Eston. Acad. Sci. Phys. Math., 39, 1–8 (1990).MathSciNetzbMATHGoogle Scholar
  13. 13.
    A. K. Ray, “On generalized 2-recurrent tensors in Riemannian spaces,” Acad. Roy. Belg., Bull. Cl. Sci., 5, No. 58, 220–228 (1972).Google Scholar
  14. 14.
    W. Roter, “On conformally recurrent Ricci-recurrent manifolds,” Colloq. Math., 46, No. 1, 45–57 (1982).MathSciNetzbMATHGoogle Scholar
  15. 15.
    S. Sasaki, Lecture Notes on Almost Contact Manifolds, Part I, Tohoku Univ. (1965).Google Scholar
  16. 16.
    M. M. Tripathi, T. Sasahara, and J.-S. Kim, “On invariant submanifolds of contact metric manifolds,” Tsukuba J. Math., 29, No. 2, 495–510 (2005).MathSciNetzbMATHGoogle Scholar
  17. 17.
    S. Tanno, “Ricci curvatures of contact Riemannian manifolds,” Tohoku Math. J., 40, 441–448 (1988).MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    K. Yano and M. Kon, “Structures on manifolds,” Ser. Pure Math., World Scientific, Singapore (1984).zbMATHGoogle Scholar
  19. 19.
    K. Yano and M. Kon, “Antiinvariant submanifolds,” Lect. Notes Pure Appl. Math., 21 (1976).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  • Avik De
    • 1
  1. 1.University of CalcuttaCalcuttaIndia

Personalised recommendations