Generalized Sasakian Manifolds: Pseudosymmetry Characterizations Related to Some Important Curvature Tensors
Abstract
In this study, generalized Sasakian space forms are examined on $W_{5}-,W_{6},W_{7}$, and $W_{9}-$ curvature tensors. Moreover, special curvature conditions with the help of $W_{5}-,W_{6},W_{7}$, $W_{9}-$ pseudosymmetry and $W_{5}-,W_{6},W_{7}$, $W_{9}-$ Ricci pseudosymmetry are defined. The behavior for the generalized Sasakian space form is then represented in accordance with these concepts.
Downloads
References
Yano, K., & Kon, M. (1984). Structures on manifolds. World Scientific. https://doi.org/10.1142/0067
Tripathi, M., & Gupta, P. (2011). $tau$-curvature tensor on a semi-Riemannian manifold. Journal of Advanced Mathematical Studies, 4(1), 117-129.
Alegre, P., Blair, D. E., & Carriazo, A. (2004). Generalized space forms. Israel Journal of Mathematics, 141, 157-183. https://doi.org/10.1007/BF02772217
Alegre, P., & Carriazo, A. (2008). Structures on generalized Sasakian space forms. Differential Geometry and Its Applications, 26, 656-666. https://doi.org/10.1016/j.difgeo.2008.04.014
Atçeken, M. (2014). On generalized Sasakian space forms satisfying certain conditions on the concircular curvature tensor. Bulletin of Mathematical Analysis and Applications, 6(1), 1-8. https://doi.org/10.11648/j.pamj.s.2015040102.18
Mert, T., & Atçeken, M. (2023). Generalized Sasakian space forms on W0-curvature tensor. Honam Mathematical Journal, 45(2), 215-230.
Belkhelfa, M., Deszcz, R., & Verstraelen, L. (2005). Symmetry properties of Sasakian space forms. Soochow Journal of Mathematics, 31, 611-616.
De, U. C., & Sarkar, A. (2010). On the projective curvature tensor of generalized Sasakian space forms. Quaestiones Mathematicae, 33, 245-252. https://doi.org/10.2989/16073606.2010.491203
De, U. C., & Sarkar, A. (2012). Some curvature properties of generalized Sasakian space forms. Lobachevskii Journal of Mathematics, 33(1), 22-27. https://doi.org/10.1134/S1995080212010088
Kim, U. K. (2006). Conformally flat generalized Sasakian space forms and locally symmetric generalized Sasakian space forms. Note di Matematica, 26, 55-67.
Sardar, A., & Sarkar, A. (2025). Different solitons associated with 3-dimensional generalized Sasakian space forms. Afrika Matematika, 36(1), Article 10. https://doi.org/10.1007/s13370-024-01233-1
AlHusseini, F. H., & Abood, H. M. (2025). Pseudo-quasi conformal curvature tensor of quasi-Sasakian manifolds with generalized Sasakian space forms. Malaysian Journal of Mathematical Sciences, 19(2), 383-398. https://doi.org/10.47836/mjms.19.2.02
Chaubey, S. K., Yadav, S., & Akyol, M. A. (2025). Generalized Sasakian space forms with a contact conformal curvature tensor. Surveys in Mathematics and Its Applications, 20, 217-233.
Nandy, S. (2024). Some properties of invariant submanifolds of generalized Sasakian space forms using curvature tensors. Journal of Computational Analysis & Applications, 33(2).
Rovenski, V. (2024). Characterization of Sasakian manifolds. Asian-European Journal of Mathematics, 17(3), 2450030. https://doi.org/10.1142/S179355712450030X
AlHusseini, F. H., & Abood, H. M. (2025). Quasi-Sasakian manifolds endowed with vanishing pseudo quasi-conformal curvature tensor. MethodsX, 15. https://doi.org/10.1016/j.mex.2025.103512

This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg)
