Honam Mathematical Journal (호남수학학술지)

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GENERALIZED SASAKIAN SPACE FORMS ON W0-CURVATURE TENSOR

  • Tugba Mert (Department of Mathematics, University of Sivas Cumhuriyet) ;
  • Mehmet Atceken (Department of Mathematics, University of Aksaray)
  • Received : 2022.05.06
  • Accepted : 2023.01.02
  • Published : 2023.06.01
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Abstract

In this article, generalized Sasakian space forms are investigated on W0 -curvature tensor. Characterizations of generalized Sasakian space forms are obtained on W0-curvature tensor. Special curvature conditions established with the help of Riemann, Ricci, concircular, projective curvature tensors are discussed on W0-curvature tensor. With the help of these curvature conditions, important characterizations of generalized Sasakian space forms are obtained. In addition, the concepts of W0-pseudosymmetry and W0 -Ricci pseudosymmetry are defined and the behavior according to these concepts for the generalized Sasakian space form is examined.

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References

  1. P. Alegre, D. E. Blair, and A. Carriazo, Generalized Sasakian space form, Israel Journal of Mathematics 141 (2004), 157-183.  https://doi.org/10.1007/BF02772217
  2. P. Alegre and A. Cariazo, Structures on generalized Sasakian-space-form, Differential Geom. and its Application 26 (2008), 656-666.  https://doi.org/10.1016/j.difgeo.2008.04.014
  3. M. At,ceken, On generalized Sasakian space forms satisfying certain conditions on the concircular curvature tensor, Bulletin of Math. Analysis and Applications 6 (2014), no. 1, 1-8 
  4. M. Belkhelfa, R. Deszcz, and L. Verstraelen, Symmetry properties of Sasakianspace-forms, Soochow Journal of Mathematics 31 (2005), 611-616. 
  5. U. C. De and A. Sarkar, On the projective curvature tensor of generalized Sasakian space forms, Quaestines Mathematicae 33 (2010), 245-252.  https://doi.org/10.2989/16073606.2010.491203
  6. U. C. De and A. Sarkar, Some curvature properties of generalized Sasakian space forms, Lobachevskii Journal of Mathematics 33 (2012), no. 1, 22-27.  https://doi.org/10.1134/S1995080212010088
  7. U. K. Kim, Conformally flat generalized Sasakian-space-forms and locally symmetric generalized Sasakian-space-forms, Note di Matemetica 26 (2006), 55-67. 
  8. T. Mert, Characterization of some special curvature tensor on almost C (α)-manifold, Asian Journal of Mathematics and Computer Research, 29 (2022), no. 1, 27-41.  https://doi.org/10.56557/ajomcor/2022/v29i17629
  9. C. Ozgur and N. M. Tripathi, On P-Sasakian manifolds satisfying certain conditions on concircular curvature tensor, Turk. J. Math. 31 (2007), 171-179. 
  10. G. T. Sreenivasa, Venkatesha, and C. S. Bagewadi, Some results on (LCS)2n+1-manifolds, Bulletin of Mathematical Analysis and Applications 1 (2009), no. 3, 64-70. 
  11. M. Tripathi and P. Gupta, τ-curvature tensor on a semi-Riemannian manifold, J. Adv. Math. Studies 4 (2011), 117-129. 
  12. P. Uygun and M. Atceken, On (κ, µ)-paracontact metric spaces satisfying some conditions on the W0-curvature tensor, New Trends in Mathematical Sciences 26 (2021), no. 2, 26-37.