De, Uday Chand;De, Biman Kanti

  • Published : 2008.07.31


The object of the present paper is to study some properties of a quasi Einstein manifold. A non-trivial concrete example of a quasi Einstein manifold is also given.


quasi Einstein manifolds;cyclic Ricci tensor;Killing vector field


  1. A. L. Besse, Einstein Manifolds, Ergeb. Math. Grenzgeb., 3. Folge, Bd. 10, Springer-Verlag, Berlin, Heidelberg, New York, 1987
  2. M. C. Chaki and R. K. Maity, On quasi Einstein manifolds, Publ. Math. Debrecen 57 (2000), 297-306
  3. M. C. Chaki, On generalized quasi-Einstein manifolds, Publ. Math. Debrecen 58 (2001), 683-691
  4. U. C. De, On quasi-Einstein manifolds, Periodica Math. Hungarica 48 (2004), 223-231
  5. U. C. De, On conformally flat special quasi-Einstein manifolds, Publ. Math. Debrecen 66 (2005), 129-136
  6. R. Deszcz, M. Glogowska, M. Hotlos, and Z. Senturk, On certain quasi-Einstein semisymmetric hypersurfaces, Annales Univ. Sci. Budapest. Eotovos Sect. Math. 41 (1998), 151-164
  7. R. Deszcz, M. Hotlos, and Z. Senturk, On curvature properties of quasi-Einstein hypersurfaces in semi-Euclidean spaces, Soochow J. Math. 27 (2001), 375-389
  8. D. Ferus, A remark on Codazzi tensors in constant curvature space, Lecture note in Mathematics, 838, Global Differential Geometry and Global Analysis, Springer Verlag, New York, (1981), p. 257
  9. S. R. Guha, On quasi-Einstein and generalized quasi-Einstein manifolds, Facta Universitatis 3 (2003), 821-842
  10. U. H. Ki and H. Nakagawa, A characterization of the Cartan hypersurfaces in a sphere, Tohoku Math. J. 39 (1987), 27-40
  11. M. Obata, Certain conditions for a Riemannian manifold to be isometric with a sphere, J. Math. Soc. Japan 14 (1962), 333-340
  12. M. Obata, Conformal transformations in Riemannian manifolds, Sigaku Math. Soc. Japan 14 (1963), 152-164
  13. M. Obata, Riemannian manifolds admitting a solution of certain system of differential equations, Proc. United States-Japan Seminar in Differential Geometry, Kyoto, Japan, 1965, pp. 101-114
  14. K. Yano, Integral Formulas in Riemannian Geometry, Marcel Dekker, New York, 1970
  15. U. C. De and G. C. Ghosh, On quasi Einstein and special quasi Einstein manifolds, Proc. of the Int. Conf. of Mathematics and its applications, Kuwait University, April 5-7, 2004, 178-191

Cited by

  1. ERRATUM TO "ON LORENTZIAN QUASI-EINSTEIN MANIFOLDS, J. KOREAN MATH. SOC. 48 (2011), NO. 4, PP. 669-689" vol.48, pp.6, 2011,
  2. On Pseudo Ricci Symmetric Manifolds vol.58, pp.1, 2012,
  3. Characterizations of mixed quasi-Einstein manifolds vol.14, pp.06, 2017,
  4. On quasi-Einstein Weyl manifolds vol.14, pp.09, 2017,
  5. Certain results on N(k)-quasi Einstein manifolds pp.2190-7668, 2018,