Ukrainian Mathematical Journal

, Volume 67, Issue 10, pp 1469–1483 | Cite as

Invariant Submanifolds of Trans-Sasakian Manifolds

  • C. S. Bagewadi
  • B. S. Anitha
Article
  • 108 Downloads

We prove the equivalence of total geodesicity, recurrence, birecurrence, generalized birecurrence, Riccigeneralized birecurrence, parallelism, biparallelism, pseudoparallelism, bipseudoparallelism of \( \sigma \) for the invariant submanifold M of the trans-Sasakian manifold \( \tilde{M} \)

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References

  1. 1.
    K. Arslan, U. Lumiste, C. Murathan, and C. Ozgur, “2-Semi-parallel surfaces in space forms. I. Two particular cases,” Proc. Eston. Acad. Sci. Phys. Math., 49, No. 3, 139–148 (2000).MathSciNetMATHGoogle Scholar
  2. 2.
    A. C. Asperti, G. A. Lobos, and F. Mercuri, “Pseudo-parallel immersions in space forms,” Math. Contemp., 17, 59–70 (1999).MathSciNetMATHGoogle Scholar
  3. 3.
    A. Turgut Vanli and R. Sari, “Invariant submanifolds of trans-Sasakian manifolds,” Different. Geom.-Dynam. Systems, 12, 177–288 (2010).MathSciNetMATHGoogle Scholar
  4. 4.
    C. S. Bagewadi and V. S. Prasad, “Invariant submanifolds of Kenmotsu manifolds,” Kuvempu Univ. Sci. J., 1, No. 1, 92–97 (2001).MathSciNetMATHGoogle Scholar
  5. 5.
    D. E. Blair, “Contact manifolds in Riemannian geometry,” Lect. Notes Math., 509 (1976).Google Scholar
  6. 6.
    D. E. Blair and J. A. Oubina, “Conformal and related changes of metric on the product of two almost contact metric manifolds,” Publ. Math., 34, No. 1, 199–207 (1990).MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    B. Y. Chen, Geometry of Submanifolds and its Applications, Sci. Univ. Tokyo, Tokyo (1981).MATHGoogle Scholar
  8. 8.
    D. Chinea and P. S. Prestelo, “Invariant submanifolds of trans-Sasakian manifolds,” Publ. Math. Debrecen, 38, No. 1-2, 103–109 (1991).MathSciNetMATHGoogle Scholar
  9. 9.
    J. Deprez, “Semi-parallel surfaces in the Euclidean space,” J. Geometry, 25, 192–200 (1985).MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    A. Gray and L. M. Hervella, “The sixteen classes of almost Hermitian manifolds and their linear invariants,” Ann. Mat. Pura Appl., 123, No. 4, 35–58 (1980).MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    J. C. Marrero, “The local structure of trans-Sasakian manifolds,” Ann. Mat. Pura ed Appl., 4, No. 162, 77–86 (1992).MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    C. Murathan, K. Arslan, and R. Ezentas, “Ricci generalized pseudo-parallel immersions,” Different. Geom. Its Appl., Matfyzpress, Prague (2005), pp. 99–108.Google Scholar
  13. 13.
    J. A. Oubina, “New classes of almost contact metric structures,” Publ. Math. Debrecen, 32, 187–193 (1985).MathSciNetMATHGoogle Scholar
  14. 14.
    C. Ozgur and C. Murathan, “On invariant submanifolds of Lorentzian para-Sasakian manifolds,” Arab. J. Sci. Eng. A, 34, No. 2, 177–185 (2008).MathSciNetGoogle Scholar
  15. 15.
    W. Roter, “On conformally recurrent Ricci-recurrent manifolds,” Colloq. Math., 46, No. 1, 45–57 (1982).MathSciNetMATHGoogle Scholar
  16. 16.
    A. A. Shaikh, K. K. Baishya, and Eyasmin, “On D-homothetic deformation of trans-Sasakian structure,” Demonstr. Math., 41, No. 1, 171–188 (2008).Google Scholar
  17. 17.
    K. Yano and M. Kon, Structures on Manifolds, World Sci., Singapore (1984).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • C. S. Bagewadi
    • 1
  • B. S. Anitha
    • 1
  1. 1.Kuvempu UniversityKarnatakaIndia

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