TY - JOUR T1 - Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons AU - Mert, Tuğba AU - Atçeken, Mehmet PY - 2025 DA - September Y2 - 2025 DO - 10.33434/cams.1708440 JF - Communications in Advanced Mathematical Sciences PB - Emrah Evren KARA WT - DergiPark SN - 2651-4001 SP - 151 EP - 159 VL - 8 IS - 3 LA - en AB - In this paper, we investigate the characterization of Lorentzian $\beta $-Kenmotsu manifolds admitting $\eta$-Ricci-Yamabe solitons. First, we examine the cases where such manifolds are Ricci pseudosymmetric and Ricci semisymmetric. Then, by employing certain special curvature tensors, we explore the concepts of Ricci pseudosymmetry and semisymmetry in greater detail and construct the geometry of the Lorentzian $\beta$-Kenmotsu manifold accordingly. KW - $\eta$-Ricci-Yamabe soliton KW - Lorentzian $\beta$-Kenmotsu manifold KW - Pseudo-symmetry CR - [1] D. G. Prakasha, C. S. Bagewadi, N. S. Basavarajappa, On pseudosymmetric Lorentzian $\alpha$-Sasakian manifolds, Int. J. Pure Appl. Math., 48 (2008), 57-65. CR - [2] G. Ingalahalli, C. S. Bagewadi, Ricci solitons $\alpha$-Sasakian manifolds, ISRN Goem., 2012(1) (2012), 1-13. https://doi.org/10.5402/2012/421384 CR - [3] V. Rajan, P.S. Gyanvendra, P. Pawan, K.M. Anand, $W_{8}$-curvature tensor in Lorentzian $\alpha$-Sasakian manifold, TURCOMAT, 11(3) (2020), 1061-1072. https://doi.org/10.17762/turcomat.v11i3.12561 CR - [4] C. S. Bagewadi, E. G. Kumar, Notes on trans-Sasakian manifolds, Tensor (N.S.), 65(1) (2004), 80-88. CR - [5] R. S. Hamilton, The Ricci flow on surfaces, Mathematics and General Relativity, 71 (1998), 237-262. CR - [6] S. Güler, M. Crasmareanu, Ricci-Yamabe maps for Riemannian flow and their volume variation and volume entropy, Turk. J. Math., 43(5) (2019), 2631-2641. https://doi.org/10.3906/mat-1902-38 CR - [7] M. D. Siddiqi, M. Akyol, $\eta$-Ricci-Yamabe solitons on Riemannian submersions from Riemannian manifolds, (2020), arXiv:14114v1[math.DG]. CR - [8] R. Seszcz, L. Verstraelen, S. Yaprak, Warped products realizing a certain condition of pseudosymmetric type imposed on the curvature tensor, Chin. J. Math., 22(2) (1994), 139-157. CR - [9] F. Zengin, S. A. Demirbağ, S. A. Uysal, H. B. Yilmaz, Some vector fields on a Riemannian manifold with semi-symmetric metric connection, Bull. Iranian Math. Soc., 38(2) (2012), 479–490. CR - [10] K. De, U. C. De, Almost quasi-Yamabe solitons and gradient almost quasi-Yamabe solitons in paracontact geometry, Quaest. Math., 44(11) (2021), 1429-1440. https://doi.org/10.2989/16073606.2020.1799882 CR - [11] R. Kundu, A. Das, A. Biswas, Conformal Ricci soliton in Sasakian manifolds admitting general connection, J. Hyperstruct., 13(1) (2024), 46-61. https://doi.org/10.22098/jhs.2024.14940.1012 CR - [12] M. Atçeken, T. Mert, P. Uygun, Ricci-Pseudosymmetric $\left( LCS\right) _{n}-$manifolds admitting almost $\eta-$Ricci solitons, Asian J. Math. Comput. Res., 29(2) (2022), 23-32. https://doi.org/10.56557/ajomcor/2022/v29i27900 CR - [13] H. Nagaraja, C. R. Premalatta, Ricci solitons in Kenmotsu manifolds, J. Math. Analysis, 3(2) (2012), 18–24. CR - [14] A. N. Siddiqui, M. D. Siddiqi, V. Vandana, Ricci solitons on $\alpha$-Sasakian manifolds with quarter symmetric metric connection, Bulletin of the Transilvania University of Braşov Series III: Mathematics and Computer Science, 4(66)(1) (2024), 175-190. https://doi.org/10.31926/but.mif.2024.4.66.1.13 CR - [15] M. D. Siddiqi, $\eta$-Einstein solitons in an $\left(\varepsilon\right) $-Kenmotsu manifolds with a semi-symmetric metric connection, Annales, Univ. Sci. Budapest, 62(LXII) (2019), 5-25. CR - [16] M. D. Siddiqi, $\eta$-Ricci solitons in $\delta$-Lorentzian trans Sasakian manifolds with a semi-symmetric metric connection, Kyungpook Math. J., 59(3) (2019), 537-562. https://doi.org/10.5666/KMJ.2019.59.3.537 CR - [17] M. Tripathi, P. Gupta, $\tau-$−curvature tensor on a semi-Riemannian manifold, J. Adv. Math. Studies, 4 (2011), 117-129. CR - [18] G. Ayar, M. Yıldırım, $\eta$-Ricci solitons on nearly Kenmotsu manifolds, Asian-Eur. J. Math., 12(6) (2019), 2040002. https://doi.org/10.1142/S1793557120400021 CR - [19] S. K. Pankaj, G. A. Chaubey, Yamabe and gradient Yamabe solitons on 3-dimensional hyperbolic Kenmotsu manifolds, Differ. Geom. Dyn. Syst, 23 (2021), 183-196. CR - [20] G. Ayar, Kenmotsu manifoldlarda konformal Ricci solitonlar, Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 19(3) (2019), 635-642. https://doi.org/10.35414/akufemubid.623574 CR - [21] Y. J. Suh, K. De, U. C. De, Compact almost Co-Kahler manifolds and Ricci-Yamabe solitons, Filomat, 38(23) (2024), 8069-8080. https://doi.org/10.2298/FIL2423069S UR - https://doi.org/10.33434/cams.1708440 L1 - https://dergipark.org.tr/en/download/article-file/4911237 ER -