Periodica Mathematica Hungarica

, Volume 59, Issue 2, pp 119–146 | Cite as

On pseudo quasi-Einstein manifolds

  • Absos Ali ShaikhEmail author


The object of the present paper is to introduce a type of non-flat semi-Riemannian manifold, called pseudo quasi-Einstein manifold and to study some geometric and global properties of such a manifold. Also the existence of such a manifold is ensured by several non-trivial examples.

Key words and phrases

pseudo quasi-Einstein manifold pseudo quasi-constant curvature conformally flat Killing vector field 

Mathematics subject classification numbers

53B05 53B15 53C15 53C25 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. K. Beem and P. E. Ehrlich, Global Lorentzian geometry, Marcel Dekker Inc., New York, 1981.zbMATHGoogle Scholar
  2. [2]
    D. E. Blair, T. Koufogiorgos and B. J. Papantoniou, Contact metric manifolds satisfying a nullity condition, Israel J. Math., 91 (1995), 189–214.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    F. Brickell and R. S. Clark, Differentiable manifolds, Van Nostrand Reinhold Comp., London, 1970.zbMATHGoogle Scholar
  4. [4]
    M. C. Chaki and R. K. Maity, On quasi-Einstein manifolds, Publ. Math. Debrecen, 57 (2000), 297–306.zbMATHMathSciNetGoogle Scholar
  5. [5]
    B. Y. Chen and K. Yano, Hypersurfaces of conformally flat spaces, Tensor (N. S.), 26 (1972), 318–322.zbMATHMathSciNetGoogle Scholar
  6. [6]
    U. C. De and G. C. Ghosh, On quasi-Einstein manifolds, Period. Math. Hungar., 48(1–2) (2004), 223–231.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    R. Deszcz and M. Hotloś, Remarks on Riemannian manifolds satisfying a certain curvature condition imposed on the Ricci tensor, Prace Nauk. Pol. Szczec., 11 (1989), 23–34.Google Scholar
  8. [8]
    R. Deszcz, F. Dillen, L. Verstraelen and L. Vrancken, Quasi-Einstein totally real submanifolds of S6(1), Tohoku Math. J., 51 (1999), 461–478.zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    R. Deszcz, M. Glogowska, M. Hotloś and Z. Sentürk, On certain quasi-Einstein semi-symmetric hypersurfaces, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 41 (1998), 153–166.Google Scholar
  10. [10]
    R. Deszcz, M. Hotloś and Z. Sentürk, Quasi-Einstein hypersurfaces in semi-Riemannian space forms, Colloq. Math., 81 (2001), 81–97.CrossRefGoogle Scholar
  11. [11]
    R. Deszcz, M. Hotloś and Z. Sentürk, On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces, Soochow J. Math., 27(4) (2001), 375–389.zbMATHMathSciNetGoogle Scholar
  12. [12]
    R. Deszcz, P. Verheyen and L. Verstraelen, On some generalized Einstein metric conditions, Publ. Inst. Math. (Beograd) (N.S.), 60:74 (1996), 108–120.MathSciNetGoogle Scholar
  13. [13]
    D. Ferus, A remark on Codazzi tensors on constant curvature space, Global Differential Geometry and Global Analysis, Lecture Notes in Math. 838, Springer-Verlag, New York, 1981.CrossRefGoogle Scholar
  14. [14]
    N. J. Hicks, Notes on Differential Geometry, Affiliated East West Press Pvt. Ltd., 1969.Google Scholar
  15. [15]
    Koufogiorgos, T. and Tsichlias, C., Generalized (k, μ)-contact metric manifolds with ∥grad k∥ = constant, J. Geom., 78 (2003), 83–91.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    A. L. Mocanu, Les variétés a courbure quasi-constant de type Vrănceanu, Lucr. Conf. Nat. de Geom. Si Top., Tirgoviste, 1987.Google Scholar
  17. [17]
    B. O’ Neill, Semi-Riemannian Geometry, Academic Press, Inc., 1983.Google Scholar
  18. [18]
    M. Novello and M. J. Reboucas, The stability of a rotating universe, The Astrophysics Journal, 225 (1978), 719–724.CrossRefGoogle Scholar
  19. [19]
    J. A. Schouten, Ricci-calculus (2nd edn.), Springer-Verlag, Berlin, 1954.zbMATHGoogle Scholar
  20. [20]
    A. A. Shaikh and K. K. Baishya, On ϕ-symmetric LP-Sasakian manifolds, Yokohama Math. J., 52 (2006), 97–112.zbMATHMathSciNetGoogle Scholar
  21. [21]
    A. A. Shaikh and K. K. Baishya, On (k, μ)-contact metric manifolds, Diff. Geom. Dyn. Syst., 8 (2006), 253–261.zbMATHMathSciNetGoogle Scholar
  22. [22]
    B. Spain, Tensor Calculus (3rd edn.), Radha Publishing House, Kolkata, 1995.Google Scholar
  23. [23]
    Gh. Vrănceanu, Lecons des Geometrie Differential, Vol. 4, Ed. de l’Academie, Bucharest, 1968.Google Scholar
  24. [24]
    Y. Watanabe, Integral inequalities in compact orientable manifolds, Riemannian or Kahlerian, Kodai Math. Sem. Rep., 20 (1968), 264–271.zbMATHCrossRefMathSciNetGoogle Scholar
  25. [25]
    K. Yano, Integral formulas in Riemannian Geometry, Marcel Dekker, New York, 1970.zbMATHGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Burdwan GolapbagBurdwanIndia

Personalised recommendations