Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons

Tuğba Mert; Mehmet Atçeken

doi:10.33434/cams.1708440

Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons

Abstract

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.

Keywords

$\eta$-Ricci-Yamabe soliton, Lorentzian $\beta$-Kenmotsu manifold, Pseudo-symmetry

References

[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.
[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
[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
[4] C. S. Bagewadi, E. G. Kumar, Notes on trans-Sasakian manifolds, Tensor (N.S.), 65(1) (2004), 80-88.
[5] R. S. Hamilton, The Ricci flow on surfaces, Mathematics and General Relativity, 71 (1998), 237-262.
[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
[7] M. D. Siddiqi, M. Akyol, $\eta$-Ricci-Yamabe solitons on Riemannian submersions from Riemannian manifolds, (2020), arXiv:14114v1[math.DG].
[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.
[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.
[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

[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
[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
[13] H. Nagaraja, C. R. Premalatta, Ricci solitons in Kenmotsu manifolds, J. Math. Analysis, 3(2) (2012), 18–24.
[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
[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.
[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
[17] M. Tripathi, P. Gupta, $\tau-$−curvature tensor on a semi-Riemannian manifold, J. Adv. Math. Studies, 4 (2011), 117-129.
[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
[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.
[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
[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

Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Tuğba Mert ^*
0000-0001-8258-8298
Türkiye

Mehmet Atçeken
0000-0002-1242-4359
Türkiye

Early Pub Date

August 13, 2025

Publication Date

September 23, 2025

Submission Date

May 28, 2025

Acceptance Date

August 11, 2025

Published in Issue

Year 2025 Volume: 8 Number: 3

DOI

https://doi.org/10.33434/cams.1708440

IZ

https://izlik.org/JA38RN58AJ

APA

Mert, T., & Atçeken, M. (2025). Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons. Communications in Advanced Mathematical Sciences, 8(3), 151-159. https://doi.org/10.33434/cams.1708440

AMA

1.Mert T, Atçeken M. Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons. Communications in Advanced Mathematical Sciences. 2025;8(3):151-159. doi:10.33434/cams.1708440

Chicago

Mert, Tuğba, and Mehmet Atçeken. 2025. “Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons”. Communications in Advanced Mathematical Sciences 8 (3): 151-59. https://doi.org/10.33434/cams.1708440.

EndNote

Mert T, Atçeken M (September 1, 2025) Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons. Communications in Advanced Mathematical Sciences 8 3 151–159.

IEEE

[1]T. Mert and M. Atçeken, “Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons”, Communications in Advanced Mathematical Sciences, vol. 8, no. 3, pp. 151–159, Sept. 2025, doi: 10.33434/cams.1708440.

ISNAD

Mert, Tuğba - Atçeken, Mehmet. “Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons”. Communications in Advanced Mathematical Sciences 8/3 (September 1, 2025): 151-159. https://doi.org/10.33434/cams.1708440.

JAMA

1.Mert T, Atçeken M. Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons. Communications in Advanced Mathematical Sciences. 2025;8:151–159.

MLA

Mert, Tuğba, and Mehmet Atçeken. “Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons”. Communications in Advanced Mathematical Sciences, vol. 8, no. 3, Sept. 2025, pp. 151-9, doi:10.33434/cams.1708440.

Vancouver

1.Tuğba Mert, Mehmet Atçeken. Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons. Communications in Advanced Mathematical Sciences. 2025 Sep. 1;8(3):151-9. doi:10.33434/cams.1708440

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Some Geometric Properties of Lorentzian $\beta$-Kenmotsu Manifolds Admitting $\eta$-Ricci-Yamabe Solitons

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Early Pub Date

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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