International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2557

Full Length Research Paper

Conformally Osserman Lorentzian manifolds satisfying a certain condition on the Ricci tensor

Mehmet ErdoÄŸan1*, Jeta Alo2 and  Beran Pirinçci3
  1Yeniyuzyil University, Faculty of Engineering, Department of Computer Engineering, Topkapi, Istanbul, Turkey. 2Beykent University, Faculty of Science and Letters, Department of Mathematics and Computing, 34457 ÅžiÅŸli, Istanbul, Turkey. 3Istanbul University, Faculty of Science, Department of Mathematics,Vezneciler, Istanbul, Turkey.
Email: [email protected]

  •  Accepted: 27 January 2011
  •  Published: 18 February 2011



Let  , , be an n-dimensional homogeneous Lorentzian manifold of which the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit timelike (spacelike) tangent vectors (known as conformally Osserman Lorentzian manifolds). Then  is a conformally Osserman Lorentzian manifold if and only if  is a conformally flat manifold, (Blazic, 2005). In this paper, by utilizing this equivalence and the similar arguments in Erdogan and Ikawa (1995)  and Sekigawa and Takagi (1971), we classify locally conformally flat homogeneous Lorentzian manifolds and, equivalently, as well as conformally Osserman Lorentzian manifolds which satisfy  a condition on the Ricci tensor.


Key words:  Conformally manifold,  Weyl conformal tensor,  conformally Osserman manifold,  conformal Jacobi operator.