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On quasi Einstein manifolds

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Abstract

In this paper we give some examples of a quasi Einstein manifold (QE)n. Next we prove the existence of (QE)n manifolds. Then we study some properties of a quasi Einstein manifold. Finally the hypersurfaces of a Euclidean space have been studied.

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References

  1. M. C. Chaki and R. K. Maity, On quasi Einstein manifold, Publ. Math. Debrecen 57 (2000), 297–306.

    MathSciNet  MATH  Google Scholar 

  2. B. Y. Chen and K. Yano, Hypersurfaces of a conformally flat space, Tensor, N.S. 26 (1972), 318–322.

    MathSciNet  MATH  Google Scholar 

  3. Gh. Vrănceanu, Lecons des Geometrie Differential, Vol. 4, Ed. de l'Academie, Bucharest, 1968.

    Google Scholar 

  4. A. L. Mocanu, Les variétés a courbure quasi-constant de type Vrănceanu, Lucr. Conf. Nat. de Geom. Si Top., Tirgoviste, 1987.

    MATH  Google Scholar 

  5. L. Verstraelen, Comments on pseudo-symmetry in the sense of R. Deszez, Geometry and Topology of Submanifolds, VI, World Scientific, 1993, 199–209.

    Google Scholar 

  6. E. M. Patterson, Some theorems on Ricci-recurrent spaces, J. London. Math. Soc. 27 (1952), 287–295.

    Article  MathSciNet  MATH  Google Scholar 

  7. L. TamÁssy and T. Q. Binh, On weak symmetries of Einstein and Sasakian manifolds, Tensor, N.S. 53 (1993), 140–148.

    MathSciNet  MATH  Google Scholar 

  8. U. C. De and S. K. Ghosh, On weakly Ricci-symmetric spaces, Publ. Math. Debrecen 60 (2002), 201–208.

    MathSciNet  MATH  Google Scholar 

  9. B. Y. Chen, Geometry of submanifolds, Marcel Dekker, Inc., New York, 1973.

    MATH  Google Scholar 

  10. T. Adati and G. Chuman, Special para-Sasakian manifolds D-conformal to a manifold of constant curvature, TRU Math. 19-2 (1983), 179–193.

    MathSciNet  MATH  Google Scholar 

  11. T. Adati and G. Chuman, Special para-Sasakian manifolds and concircular transformations, TRU Math. 20-1 (1984), 111–123.

    MathSciNet  MATH  Google Scholar 

  12. T. Adati and T. Miyazawa, On paracontact Riemannian manifolds, TRU Math. 13-2 (1977), 27–39.

    MathSciNet  MATH  Google Scholar 

  13. G. Chuman, D-conformal changes in para-Sasakian manifolds, Tensor, N.S. 39 (1982), 117–123.

    MathSciNet  MATH  Google Scholar 

  14. R. Deszcz, On pseudosymmetric spaces, Bull. Belg. Math. Soc. Ser A, 44 (1992), 1–34.

    MathSciNet  MATH  Google Scholar 

  15. L. P. Eisenhart, Riemannian Geometry, Princeton University Press, 1949.

  16. J. A. Schouten, Über die konforme Abbildung n-dimensionaler Mannigfaltigkeiten mit quadratischer Massbestimmung auf eine Mannigfaltigkeit mit euklidischer Massbestimmung, Math. Z. 11 (1921), 58–88.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Kalyani, Kalyani, 741235, West Bengal, India

    U. C. De & Gopal Chandra Ghosh

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  1. U. C. De
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  2. Gopal Chandra Ghosh
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De, U.C., Ghosh, G.C. On quasi Einstein manifolds. Periodica Mathematica Hungarica 48, 223–231 (2004). https://doi.org/10.1023/B:MAHU.0000038977.94711.ab

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  • DOI: https://doi.org/10.1023/B:MAHU.0000038977.94711.ab

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