Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지

On Lorentzian α-Sasakian Manifolds

  • Yildiz, Ahmet (Dumlupinar University, Art and Science Faculty, Department of Mathematics) ;
  • Murathan, Cengizhan (Uludag University, Art and Science Faculty, Department of Mathematics)
  • Received : 2004.01.07
  • Published : 2005.03.23
Download PDF
⟨ Previous Next ⟩

Abstract

The present paper deals with Lorentzian ${\alpha}-Sasakian$ manifolds with conformally flat and quasi conform ally flat curvature tensor. It is shown that in both cases, the manifold is locally isometric with a sphere $S^{2^{n}+1}(c)$. Further it is shown that an Lorentzian ${\alpha}-Sasakian$ manifold with R(X, Y).C = 0 is locally isometric with a sphere $S^{2^{n}+1}(c)$, where c = ${\alpha}^2$.

Keywords

References

  1. Lectures Notes in Mathematics v.509 Contact manifolds in Riemannian geometry Blair, D.E.
  2. Indian J. Math. v.5 On Conformally Symmetric Spaces Chaki, M.C.;Gupta, B.
  3. Bull. of Yamagata Univ. Nat. Sci. v.12 no.2 On Lorentzian paracontact manifolds Matsumoto, K.
  4. On Lorentzian P-Sasakian manifolds, Classical Analysis Mihai, I.;Rosca, R.
  5. Tensor, N. S. v.47 On a certain transformation in a Lorentzian para-Sasakian manifold Matsumoto, K.;Mihai, I.
  6. On Lorentzian para-Sasakian Manifolds Mihai, I.;Shaikh, A.A.;De, U.C.
  7. Proc. of the Coll. on Differential Geo. On Lorentzian para-Sasakian Manifolds, Syeps in Diff. Geo. Tarafdar, M.;Bhattacharyya, A.
  8. Kyungpook Math. J. v.43 Ricci Tensor in 3-dimensional Trans-Sasakian Manifolds De, U.C.;Tripathi, M.M.
  9. Tohoku Math. J. v.21 The automorphism groups of almost contact Riemannian manifolds Tanno, S.
  10. J. Korean Math. Soc. v.39 no.6 On generalized Ricci-recurrent trans-Sasakian manifolds Kim, J.S.;Prasad, R.;Tripathi, M.M.
  11. Publ. Math. Debrecen v.32 no.3-4 New classes of contact metric structures Oubina, J.A.
  12. Nepali Math. Sci. Rep. v.18 no.1-2 Trans-Sasakian manifolds are generalized quasi-Sasakian Tripathi, M.M.
  13. Ann. Mat. Pura Appl. v.123 no.4 The sixteen classes of almost Hermitian manifolds and their linear invariants Gray, A.;Hervella, L.M.
  14. Kodai Math. J. v.4 Almost contact structures and curvature tensors Janssens, D.;Vanhacke, L.
  15. Proceedings of the XIIth Portuguese-Spanish Conference on Mathematics v.II Curvature relations in trans-Sasakian manifolds Chinea, D.;Gonzales, C.
  16. Ann. Mat. Pura Appl. v.162 no.4 The local structure of trans-Sasakian manifolds Marrero, J.C.
  17. Almost contact metric manifolds, Monograph 1 Mishra, R.S.
  18. Proceedings of the XIVth Spanish-Portuguese Conference on Mathematics v.I-III On trans-Sasakian manifolds Marrero, J.C.;Chinea, D.
  19. Tohoku Math. J. v.24 A class of almost contact Riemannian manifolds Kenmotsu, K.
  20. Progress in Mathematics 155 Locally conformal Kaehler geometry Dragomir, S.;Ornea, L.
  21. Publications Matematiques v.34 Conformal and related changes of metric on the product of two almost contact metric manifolds Blair, D.E.;Oubina, J.A.