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CLASSIFICATION OF THREE-DIMENSIONAL CONFORMALLY FLAT QUASI-PARA-SASAKIAN MANIFOLDS

  • Erken, Irem Kupeli (Department of Mathematics, Faculty of Engineering and Natural Sciences, Bursa Technical University)
  • Received : 2018.11.14
  • Accepted : 2019.03.11
  • Published : 2019.09.25

Abstract

The aim of this paper is to study three-dimensional conformally flat quasi-para-Sasakian manifolds. First, the necessary and sufficient conditions are provided for three-dimensional quasipara-Sasakian manifolds to be conformally flat. Next, a characterization of three-dimensional conformally flat quasi-para-Sasakian manifold is given. Finally, a method for constructing examples of three-dimensional conformally flat quasi-para-Sasakian manifolds is presented.

Keywords

quasi-para-Sasakian manifold;conformally flat;constant curvature

References

  1. C L. Bejan and M. Crasmareanu, Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry, Ann. Global. Anal. Geom. 46 (2014), 117-127. https://doi.org/10.1007/s10455-014-9414-4
  2. D E. Blair, The theory of quasi-Sasakian structures, J. Differential Geom. 1 (1967), 331-345. https://doi.org/10.4310/jdg/1214428097
  3. D E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics 203, Birkhauser, Boston, 2002.
  4. B. Cappelletti-Montano, I. Kupeli Erken and C. Murathan, Nullity conditions in paracontact geometry, Diff. Geom. Appl. 30 (2012), 665-693. https://doi.org/10.1016/j.difgeo.2012.09.006
  5. P. Dacko and Z. Olszak, On conformally flat almost cosymplectic manifolds with Kaehlerian leaves, Rend. Sem. Mat. Univ. Poi. Torino 56 (1998), 89-103.
  6. P. Dacko, On almost para-cosymplectic manifolds, Tsukuba J. Math. 28 (2004), 193-213. https://doi.org/10.21099/tkbjm/1496164721
  7. S. Erdem, On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (${\varphi},{\varphi}'$) -holomorphic maps between them, Houston J. Math. 28 (2002), 21-45.
  8. S. Kanemaki, Quasi-Sasakian manifolds,Tohoku Math. J. 29 (1977), 227-233. https://doi.org/10.2748/tmj/1178240654
  9. S. Kaneyuki and FL. Williams, Almost paracontact and parahodge structures on manifolds, Nagoya Math. J. 99 (1985), 173-187. https://doi.org/10.1017/S0027763000021565
  10. I. Kupeli Erken, Some classes of 3-dimensional normal almost paracontact metric manifolds, Honam Math. J. 37 (2015), 457-468. https://doi.org/10.5831/HMJ.2015.37.4.457
  11. I. Kupeli Erken, On normal almost paracontact metric manifolds of dimension 3, Facta Univ. Ser. Math. Inform. 36 (2015), 777-788.
  12. I. Kupeli Erken, P. Dacko and C. Murathan, Almost ${\alpha}$-paracosymplectic manifolds, J. Geom. Phys. 88 (2015), 30-51. https://doi.org/10.1016/j.geomphys.2014.09.011
  13. I. Kupeli Erken, Curvature properties of quasi-para-Sasakian manifolds, Int. Electron. J. Geom., (to appear)
  14. Z. Olszak, Curvature properties of quasi-Sasakian manifolds, Tensor 38 (1982), 19-28.
  15. Z. Olszak, Normal almost contact metric manifolds of dimension three, Ann. Polon. Math. XLVII (1986), 41-50.
  16. Z. Olszak, On three-dimensional conformally flat quasi-Sasakian manifolds, Period Math. Hungar. 33 (1996), 105-113. https://doi.org/10.1007/BF02093508
  17. S. Tanno, Quasi-Sasakian structures of rank 2p + 1, J. Differential Geom. 5 (1971), 317-324. https://doi.org/10.4310/jdg/1214429995
  18. J. Welyczko, On basic curvature identities for almost (para)contact metric manifolds, Available in Arxiv: 1209.4731 [math. DG].
  19. J. Welyczko, On Legendre Curves in 3-Dimensional Normal Almost Paracontact Metric Manifolds, Result Math. 54 (2009), 377-387. https://doi.org/10.1007/s00025-009-0364-2
  20. S. Zamkovoy, Canonical connections on paracontact manifolds, Ann. Glob. Anal. Geom. 36 (2009), 37-60. https://doi.org/10.1007/s10455-008-9147-3
  21. S. Zamkovoy and G. Nakova, The decomposition of almost paracontact metric manifolds in eleven classes revisited, J.Geom. (2018), doi.org/10.1007/s00022-018-0423-5. https://doi.org/10.1007/s00022-018-0423-5