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A note on slant submanifolds of nearly trans-Sasakian manifolds

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Mathematica Slovaca

Abstract

The geometry of slant submanifolds of a nearly trans-Sasakian manifold is studied when the tensor field Q is parallel. It is proved that Q is not parallel on the submanifold unless it is anti-invariant and thus the result of [CABRERIZO, J. L.—CARRIAZO, A.—FERNANDEZ, L. M.—FERNANDEZ, M.: Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125–138] and [GUPTA, R. S.—KHURSHEED HAIDER, S. M.—SHARFUDIN, A.: Slant submanifolds of a trans-Sasakian manifold, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47 (2004), 45–57] are generalized.

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References

  1. AL-SOLAMY, F. R.: CR-submanifold of nearly trans-Sasakian manifold, Int. J. Math. Math. Sci. 31 (2002), 167–175.

    Article  MATH  MathSciNet  Google Scholar 

  2. BEJANCU, A.—PAPAGHIUC, N.: Semi-slant submanifolds of a Sasakian manifold, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 27 (1981), 163–170.

    MathSciNet  Google Scholar 

  3. BLAIR, D. E.: Contact Manifolds in Riemannian Geometry. Lecture Notes in Math. 509, Springer Verlag, Berlin, 1976.

    MATH  Google Scholar 

  4. BLAIR, D. E.: Geometry of Manifolds with structure group u(n) × θ(s), J. Differential Geom. 4 (1970), 155–167.

    MATH  MathSciNet  Google Scholar 

  5. BLAIR, D. E.—OUBINA, J. A.: Conformal and related changes of metric on the product of two almost contact metric manifolds, Publ. Mat. 34 (1990), 199–207.

    MATH  MathSciNet  Google Scholar 

  6. CABRERIZO, J. L.—CARRIAZO, A.—FERNANDEZ, L. M.—FERNANDEZ, M.: Slant submanifolds in Sasakian manifolds, Glasg. Math. J. 42 (2000), 125–138.

    Article  MATH  MathSciNet  Google Scholar 

  7. CHEN, B. Y.: Geometry of Slant Submanifolds, Katholieke Universiteit, Leuven, 1990.

    MATH  Google Scholar 

  8. GHERGHE, C.: Harmonicity of nearly trans-Sasakian manifolds, Demonstratio Math. 33 (2000), 151–157.

    MATH  MathSciNet  Google Scholar 

  9. GRAY, A.—HERVELLA, L. M.: The sixteen classes of almost Hermitian manifolds and their linear invariant, Ann. Mat. Pura. Appl. (4) 123 (1980), 35–58.

    Article  MATH  MathSciNet  Google Scholar 

  10. GUPTA, R. S.—KHURSHEED HAIDER, S. M.—SHARFUDIN, A.: Slant submanifolds of a trans-Sasakian manifold, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 47 (2004), 45–57.

    MathSciNet  Google Scholar 

  11. KHAN, V. A.—KHAN, M. A.—UDDIN, S.: Totally umbilical semi-invariant submanifolds of a nearly trans-Sasakian manifold, Port. Math. (N.S.) 64 (2007), 67–74.

    MATH  MathSciNet  Google Scholar 

  12. KIM, J. S.—XIMIN, L.—TRIPATHI, M. M.: On semi-invariant submanifolds of nearly trans-Sasakian manifold, Int. J. Pure Appl. Math. Sci. 1 (2004), 15–34.

    MATH  Google Scholar 

  13. KOBAYASHI, M.: CR-Submanifolds of a Sasakian manifold, Tensor (N.S.) 35 (1981), 297–307.

    MATH  MathSciNet  Google Scholar 

  14. LOTTA, A.: Slant submanifolds in contact geometry, Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 39 (1996), 353–366.

    Google Scholar 

  15. MARRERO, J. C.: The local structure of trans-Sasakian manifolds, Ann. Mat. Pura. Appl. 4 (1992), 77–86.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, King AbdulAziz University, P. O. Box 80015, Jeddah, 21589, Saudi Arabia

    Falleh R. Al-Solamy & Viqar Azam Khan

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  1. Falleh R. Al-Solamy
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  2. Viqar Azam Khan
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Correspondence to Falleh R. Al-Solamy.

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Communicated by Michal Fečkan

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Al-Solamy, F.R., Khan, V.A. A note on slant submanifolds of nearly trans-Sasakian manifolds. Math. Slovaca 60, 129–136 (2010). https://doi.org/10.2478/s12175-009-0172-x

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  • DOI: https://doi.org/10.2478/s12175-009-0172-x

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