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ALMOST α-COSYMPLECTIC f-MANIFOLDS ENDOWED WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Received : 2019.07.12
  • Accepted : 2019.10.01
  • Published : 2020.03.25

Abstract

In this paper, we introduce almost α-Cosymplectic f-manifolds endowed with a semi-symmetric non-metric connection and give some general results concerning the curvature of such connection. In particular, we study some curvature properties of an almost α-cosymplectic f-manifold equipped with semi-symmetric non-metric connection.

Keywords

References

  1. Agashe N.S., Chafle M.R., A semi-symmetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math. 23 (1992), no:6, 399-409.
  2. Akyol M. A., Vanli A. T. and Fernandez L. M., Semi-symmetric properties of Smanifolds endowed with a semi-symmetric non-metric connection, Annals of the Alexandru Ioan Cuza University-Mathematics. DOI: 10.2478/aicu-2013-0039,, Tomul LX1, f.2, 445-464, (2015).
  3. Akyol M. A., Fernandez L. M. and Martin A. P., The L-sectional curvature of S-manifolds, Konuralp Journal of Mathematics, Vol. 4, No. 1, 246-253, (2016).
  4. Akyol M. A., Sari R., On CR-submanifolds of S-manifolds endowed with a semisymmetric non-metric connection, Commun. Fak. Sci. Univ. Ser. A1. Math. Stat. Vol:65, No:1, 171-185, (2016).
  5. Akyol M. A., Beyendi S., Riemannian submersions endowed with a semisymmetric non-metric connection, Konuralp Journal of Mathematics, Vol. 6, No. 1, 188-193, (2018).
  6. Ozturk H., Murathan C., Aktan N., Vanli A.T., Almost $\alpha$-cosymplectic fmanifolds Analele stiintifice ale universitatii 'AI.I Cuza' Di iasi (S.N.) Matematica, Tomul LX, f.1.(2014).
  7. Blair D.E., Geometry of Manifolds with structural group U(n) $\times$ O(s), J.Differential Geometry, 4 (1970), 155-167. https://doi.org/10.4310/jdg/1214429380
  8. Blair D.E., Ludden G.D., Hypersurfaces in almost contact manifolds, Tohoku Math. J., 21 (1969), 354-362. https://doi.org/10.2748/tmj/1178242948
  9. Biswas S.C., De U.C., On a type of semi-symmetric non-metric connection on a Riemannian manifold, Ganita, 48 (1997), 9194.
  10. De U.C., Kamilya D., Hypersurfaces of a Riemannian manifold with semisym-metric non-metric connection, J. Indian Inst. Sci., 75 (1995), 707-710.
  11. Erken K.I, Dacko P., and Murathan C. Almost $\alpha$-paracosymplectic manifolds, arXiv: 1402.6930v1 [Math:DG] 27 Feb 2014.
  12. Sengupta J., De U.C., Binh T.Q., On a type of semi-symmetric non-metric connection on a Riemannian manifold, Indian J. Pure Appl. Math., 31 (2000), 1659-1670.
  13. Dogru Y., ozgur C., Murathan C., Riemannian manifolds with a semisymmetric non-metric connection satisfying some semisymmetry conditions, Bull. Math. Anal. Appl., 3 (2011), 206-212.
  14. Friedmann A., Schouten J.A., Uber die Geometrie der halbsymmetrischen Uber-tragungen, Math. Z., 21 (1924), 211-223. https://doi.org/10.1007/BF01187468
  15. Goldberg S.I. and Yano K., On normal globally framed f-manifolds, Tohoku Math. J., 22 (1970), 362-370. https://doi.org/10.2748/tmj/1178242763
  16. Goldberg S.I., Yano K., Globally framed f-manifolds, Illinois J. Math., 15 (1971), 456-474. https://doi.org/10.1215/ijm/1256052614
  17. Hayden H.A., Subspaces of a space with torsion, Proc. London Math. Soc., 34 (1932), 27-50. https://doi.org/10.1112/plms/s2-34.1.27
  18. Yano K., Kon M., Structures on Manifolds, 3. World Scientific Publishing Co., Singapore, 1984.
  19. Yano K., On a structure defined by a tensor field f of type (1,1) satisfying $f^3+f=0$, Tensor (N.S.), 14 (1963), 99-109.
  20. Yano K., On semi-symmetric metric connection, Rev. Roumaine Math. Pures Appl., 15 (1970), 1579-1586.
  21. Perktas S.Y., Kilic E., Keles, S. On a semi-symmetric non-metric connection in an LP-Sasakian manifold, Int. Electron. J. Geom., 3 (2010), 15-25.
  22. Ozgur C., Mihai A., Chen inequalities for submanifolds of real space forms with a semi-symmetric non-metric connection, Canad. Math. Bull., 55 (2012), 611-622. https://doi.org/10.4153/CMB-2011-108-1
  23. Sular S., Chen inequalities for submanifolds of generalized space forms wih semisymmetric non-metric connections, Turk. J. Math., 2011, DOI:10.3906/mat110-120.
  24. Sular S., Ozgur C., Generalized Sasakian space forms with semi-symmetric nonmetric connections, Proc. Est. Acad. Sci., 60 (2011), 251-257. https://doi.org/10.3176/proc.2011.4.05