Bulletin of the Iranian Mathematical Society

, Volume 44, Issue 6, pp 1387–1404 | Cite as

External Geometry of Submanifolds in Conformal Kenmotsu Manifolds

  • Roghayeh AbdiEmail author
  • Esmaiel Abedi
Original Paper


The object of the present paper is to study submanifolds of a conformal Kenmotsu manifold of which the second fundamental form is recurrent, 2-recurrent or generalized 2-recurrent. Finally, we present an example to verify our results.


Conformal Kenmotsu manifold Recurrent tensor field Totally geodesic Totally umbilic 

Mathematics Subject Classification

Primary 53C25 Secondary 53C40 


  1. 1.
    Abdi, R., Abedi, E.: Invariant and anti-invariant submanifolds of a conformal Kenmotsu manifold. Azerbaijan J. Math. 5, 54–63 (2015)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Abdi, R., Abedi, E.: \( CR \)-hypersurfaces of a conformal Kenmotsu manifold satisfying certain shape operator conditions. Period. Math. Hungar. 73(1), 83–92 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Blair, D.E.: Riemannian Geometry of Contact and Symplectic Manifolds. Birkhauser, Boston (2002)CrossRefGoogle Scholar
  4. 4.
    Chen, B.Y.: Geometry of warped products as Riemannian submanifolds and related problems. Soochow J. Math. 28, 125–156 (2002)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Chen, B.Y.: Geometry of Submanifolds and its Applications. Science University of Tokyo, Tokyo (1981)zbMATHGoogle Scholar
  6. 6.
    De, U.C., Mandal, D., Mandal, K.: Some characterizations of Kenmotsu manifolds admitting a quarter-symmetric metric connection. Bull. Transilv. Univ. Brasov Ser. III Math. Inf. Phys. 9(58)(1), 39–52 (2016)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Gray, A., Hervella, L.M.: Sixteen classes of almost Hermitian manifold and their linear invariants. Ann. Math. Pure Appl. 123(3), 35–58 (1980)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kenmotsu, K.: A class of almost contact Riemannian manifolds. Tôhoku Math. J. 24, 93–103 (1972)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Kobayashi, M.: Semi-invariant submanifolds of a certain class of almost contact manifolds. Tensor (NS) 43(1), 28–36 (1986)MathSciNetzbMATHGoogle Scholar
  10. 10.
    O’ Neill, B.: Semi-Riemannian geometry with applications to relativity. Pure and applied mathematics, vol. 103. Academic Press, Inc. [Harcourt Brace Jo-vanovich, Publishers], New York (1983)Google Scholar
  11. 11.
    Roter, W.: On conformally recurrent Ricci-recurrent manifolds. Colloq. Math. 46(1), 45–57 (1982)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Sular, S., Özgür, C.: On some submanifolds of Kenmotsu manifolds. Chaos Solitons Fractals 42, 1990–1995 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Iranian Mathematical Society 2018
corrected publication 2018

Authors and Affiliations

  1. 1.Department of MathematicsAzarbaijan shahid Madani UniversityTabrizIran

Personalised recommendations