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Invariant Submanifolds of Trans-Sasakian Manifolds

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Ukrainian Mathematical Journal Aims and scope

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. 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).

    MathSciNet  MATH  Google Scholar 

  2. A. C. Asperti, G. A. Lobos, and F. Mercuri, “Pseudo-parallel immersions in space forms,” Math. Contemp., 17, 59–70 (1999).

    MathSciNet  MATH  Google Scholar 

  3. A. Turgut Vanli and R. Sari, “Invariant submanifolds of trans-Sasakian manifolds,” Different. Geom.-Dynam. Systems, 12, 177–288 (2010).

    MathSciNet  MATH  Google Scholar 

  4. C. S. Bagewadi and V. S. Prasad, “Invariant submanifolds of Kenmotsu manifolds,” Kuvempu Univ. Sci. J., 1, No. 1, 92–97 (2001).

    MathSciNet  MATH  Google Scholar 

  5. D. E. Blair, “Contact manifolds in Riemannian geometry,” Lect. Notes Math., 509 (1976).

  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).

    Article  MathSciNet  MATH  Google Scholar 

  7. B. Y. Chen, Geometry of Submanifolds and its Applications, Sci. Univ. Tokyo, Tokyo (1981).

    MATH  Google Scholar 

  8. D. Chinea and P. S. Prestelo, “Invariant submanifolds of trans-Sasakian manifolds,” Publ. Math. Debrecen, 38, No. 1-2, 103–109 (1991).

    MathSciNet  MATH  Google Scholar 

  9. J. Deprez, “Semi-parallel surfaces in the Euclidean space,” J. Geometry, 25, 192–200 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  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).

    Article  MathSciNet  MATH  Google Scholar 

  11. J. C. Marrero, “The local structure of trans-Sasakian manifolds,” Ann. Mat. Pura ed Appl., 4, No. 162, 77–86 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Murathan, K. Arslan, and R. Ezentas, “Ricci generalized pseudo-parallel immersions,” Different. Geom. Its Appl., Matfyzpress, Prague (2005), pp. 99–108.

  13. J. A. Oubina, “New classes of almost contact metric structures,” Publ. Math. Debrecen, 32, 187–193 (1985).

    MathSciNet  MATH  Google Scholar 

  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).

    MathSciNet  Google Scholar 

  15. W. Roter, “On conformally recurrent Ricci-recurrent manifolds,” Colloq. Math., 46, No. 1, 45–57 (1982).

    MathSciNet  MATH  Google Scholar 

  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).

  17. K. Yano and M. Kon, Structures on Manifolds, World Sci., Singapore (1984).

    MATH  Google Scholar 

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 10, pp. 1309–1320, October, 2015.

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Bagewadi, C.S., Anitha, B.S. Invariant Submanifolds of Trans-Sasakian Manifolds. Ukr Math J 67, 1469–1483 (2016). https://doi.org/10.1007/s11253-016-1166-9

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  • DOI: https://doi.org/10.1007/s11253-016-1166-9

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