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SOME NOTES ON NEARLY COSYMPLECTIC MANIFOLDS

  • Received : 2021.04.26
  • Accepted : 2021.06.03
  • Published : 2021.09.25

Abstract

In this paper, we study some symmetric and recurrent conditions of nearly cosymplectic manifolds. We prove that Ricci-semisymmetric and Ricci-recurrent nearly cosymplectic manifolds are Einstein and conformal flat nearly cosymplectic manifold is locally isometric to Riemannian product ℝ × N, where N is a nearly Kähler manifold.

Keywords

References

  1. Ayar, G., Tekin, P., Aktan, N.: Some curvature conditions on Nearly Cosymplectic manifolds, Indian Journal of Industrial and Applied Mathematics, 10(1)2019, 51-58. https://doi.org/10.5958/1945-919x.2019.00004.5
  2. Blair, D.E., Almost Contact Manifolds with Killing Structure Tensors I., Pac. J. Math. 39(1971), 285-292. https://doi.org/10.2140/pjm.1971.39.285
  3. Blair D. E., Showers D. K., Yano K., Nearly Sasakian structure, Kodoi math. Sem.Rep. 27(1)(1976), 175-180.
  4. De U.C., Guha N., On generalized recurrent manifolds, Proc. Math. Soc., 7(1991), 7-11.
  5. Dundar, A., Aktan, N.: Some Results on Nearly Cosymplectic Manifolds, Universal Journal of Mathematics and Applications, 2(4) (2019), 218-223.
  6. Endo, H., On the Curvature Tensor of Nearly Cosymplectic Manifolds of Constant ϕ-sectional curvature. An. Stiit. Univ. "Al. I. Cuza" Iasi. Mat. (N.S.), (2005), 439-454.
  7. Ghosh, D., On projective recurrent spaces of second order, Acad. Roy. Belg. Bull. Cl. Sci. (5)56(1970), 1093-1099.
  8. Linchnerowicz, A., Courbure, nombres de Betti, et espaces symmetriques, Proc. Int. Cong. Math. 2(1950), 216-233.
  9. H.S. Ruse, A Classification of K4 space, London Mathematical Society, 53 (1951), 212-229. https://doi.org/10.1112/plms/s2-53.3.212
  10. Q. Khan, On generalized recurrent Sasakian manifolds, Kyungpook Math. J., 44(2004),167- 172.
  11. De Nicola, A., Dileo, G. & Yudin, I., On Nearly Sasakian and Nearly Cosymplectic Manifolds, Annali di Matematica,(2007), https://doi.org/10.1007/s10231-017-0671-2.
  12. Patterson, E. M., Some theorems on Ricci-recurrent spaces, J. London. Math. Soc. 27(1952), 287-295. https://doi.org/10.1112/jlms/s1-27.3.287
  13. Roter, W., On conformally symmetric Ricci-recurrent spaces, Colloquium Mathematicum., 31(1974), 87-96. https://doi.org/10.4064/cm-31-1-87-96
  14. Yano K., Concircular geometry I. concircular transformations, Proc. Imp. Acad. Tokyo,16(1940), 195-200.
  15. Yildirim, M., Ayar, G.: Nearly Cosymplectic Manifolds with nullity condition, Asian-Europan Journal of Mathematics, 12(6)(2019),2040012. https://doi.org/10.1142/S1793557120400124
  16. Yildirim, M. : Yakla,sik kosimplektik manifoldlar uzerinde η-Ricci solitonlar, Erzincan University Journal of Science and Technology, 13(2020), 56-62.
  17. Yildirim, M., Ayar, G.: Ricci solitons and gradient Ricci solitons on nearly cosymplectic manifolds, Journal of Universal Math., 4 (2) (2021), 201-208.
  18. Walker, A.G., On Ruses Spaces of Recurrent curvature, Proc. London Math. Soc., 52(1976), 36-64.