Pseudosymmetric Characterizations for Sasakian Manifolds Admitting General Connection
Abstract
In this study, the geometry of Sasakian manifolds is investigated using a general connection instead of the classical Levi-Civita connection. On a Sasakian manifold admitting a general connection, we first define the projective and concircular curvature tensors and obtain the characterizations of projectively flat, concircularly flat, projectively semi-symmetric, and concircularly semi-symmetric Sasakian manifolds. Additionally, by discuss the act of projective and concircular curvature tensors on each other, we reveal the properties of Sasakian manifolds admitting a general connection. In the next section, we construct Ricci-Bourguignon solitons on Sasakian manifolds admitting a general connection. In this connection, we search Ricci pseudo-symmetric, projectively Ricci pseudo-symmetric, and concircularly Ricci pseudo-symmetric Sasakian manifolds admitting Ricci-Bourguignon solitons. Consequently, we compare all these important properties on Sasakian manifolds separately according to the Tanaka-Webster, Schouten-van Kampen, and Zamkovoy connections.
References
Biswas, A., & Baishya, K. K. (2019). Study on generalized pseudo (Ricci) symmetric Sasakian manifold admitting general connection. Bulletin of the Transilvania University of Brasov, 12(2).
Biswas, A., & Baishya, K. K. (2019). A general connection on Sasakian manifolds and the case of almost pseudo symmetric Sasakian manifolds. Scientific Studies and Research Series Mathematics and Informatics, 29(1).
Golab, S. (1975). On semi-symmetric and quarter-symmetric linear connections. Tensor (N.S.), 29, 249-254.
Biswas, A., Das, S., & Baishya, K. K. (2018). On Sasakian manifolds satisfying curvature restrictions with respect to quarter symmetric metric connection. Scientific Studies and Research Series Mathematics and Informatics, 28(1), 29-40. https://doi.org/10.1097/01.COT.0000529898.02484.2e
Schouten, J. A., & Van Kampen, E. R. (1930). Zur Einbettungs-und Krummungstheorie nichtholonomer Gebilde. Mathematische Annalen, 103, 752-783. https://doi.org/10.1007/BF01455718
Tanno, S. (1969). The automorphism groups of almost contact Riemannian manifold. Tohoku Mathematical Journal, 21, 21-38. https://doi.org/10.2748/tmj/1178243031
Zamkovoy, S. (2008). Canonical connections on paracontact manifolds. Annals of Global Analysis and Geometry, 36(1), 37-60. https://doi.org/10.1007/s10455-008-9147-3
Güler, S., & Crasmareanu, M. (2019). Ricci-Yamabe maps for Riemannian flow and their volume variation and volume entropy. Turkish Journal of Mathematics, 43, 2631-2641. https://doi.org/10.3906/mat-1902-38
Hamilton, R. S. (1998). The Ricci flow on surfaces. In Mathematics and general relativity (Vol. 71, pp. 237-262). https://doi.org/10.1090/conm/071/954419
Hamilton, R. S. (1989). Lectures on geometric flows (Unpublished).
Catino, G., & Mazzieri, L. (2016). Gradient Einstein solitons. Nonlinear Analysis, 132, 66-94. https://doi.org/10.1016/j.na.2015.10.021
Naik, D. M., Venkatesha, V., & Kumara, H. A. (2020). Ricci solitons and certain related metrics on almost co-Kaehler manifolds. Journal of Mathematical Physics Analysis and Geometry, 16, 402-417. https://doi.org/10.15407/mag16.04.402
Chen, B. Y., & Deshmukh, S. (2018). A note on Yamabe solitons. Balkan Journal of Geometry and Its Applications, 23, 37-43.
Chen, B. Y., & Deshmukh, S. (2018). Yamabe and quasi-Yamabe solitons on Euclidean submanifolds. Mediterranean Journal of Mathematics, 15, 1-9. https://doi.org/10.1007/s00009-018-1237-2
De, K., & De, U. C. (2021). Almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in paracontact geometry. Quaestiones Mathematicae, 44, 1429-1440. https://doi.org/10.2989/16073606.2020.1799882
Kundu, R., Das, A., & Biswas, A. (2024). Conformal Ricci soliton in Sasakian manifolds admitting general connection. Journal of Hyperstructures, 13(1), 46-61.
Atçeken, M., Mert, T., & Uygun, P. (2022). Ricci-pseudosymmetric (LCS) -manifolds admitting almost η-Ricci solitons. Asian Journal of Mathematics and Computer Research, 29(2), 23-32. https://doi.org/10.56557/ajomcor/2022/v29127900
Nagaraja, H., & Premalatta, C. R. (2012). Ricci solitons in Kenmotsu manifolds. Journal of Mathematical Analysis, 3(2), 18-24.
Siddiqui, A. N., Siddiqi, M. D., & Vandana, V. (2024). Ricci solitons on a-Sasakian manifolds with quarter symmetric metric connection. Bulletin of the Transilvania University of Braşov Series III: Mathematics and Computer Science, 4(66)(1) 175-190. https://doi.org/10.31926/but.mif.2024.4.66.1.13
Hakami, A. H., Siddiqi, M. D., Siddiqui, A. N., & Ahmad, K. (2023). Solitons equipped with a semi-symmetric metric connection with some applications on number theory. Mathematics, 11(21), 44-52. https://doi.org/10.3390/math11214452
Siddiqi, Μ. D. (2019). η-Einstein solitons in an (8)-Kenmotsu manifolds with a semi-symmetric metric connection. Annales Universitatis Scientiarum Budapestinensis, 62 (LXII), 5-25.
Siddiqi, M. D. (2019). η-Ricci solitons in 8-Lorentzian trans Sasakian manifolds with a semi-symmetric metric connection. Kyungpook Mathematical Journal, 59(3), 537-562.
Siddiqi, M. D., & Akyol, M. (2020). η-Ricci-Yamabe solitons on Riemannian submersions from Riemannian manifolds. arXiv preprint, arXiv:14114v1 [math.DG]. https://arxiv.org/abs/14114v1
Altunbaş, M. (2025). Ricci solitons on concircularly flat and Wi-flat Sasakian manifolds admitting a general connection. Malaya Journal of Mathematics, 13(01), 8-14. https://doi.org/10.26637/mjm1301/002
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
