Conformal $\eta$-Ricci-Yamabe solitons on submanifolds of an $(LCS)_n$-manifold admitting a quarter-symmetric metric connection

Year 2024, Volume: 73 Issue: 3, 611 - 629, 27.09.2024

Sunıl Yadav , Abdul Haseeb , Ahmet Yıldız

https://doi.org/10.31801/cfsuasmas.1382928

Abstract

This paper presents some results for conformal $\eta$-Ricci-Yamabe solitons (CERYS) on invariant and anti-invariant submanifolds of a $(LCS)_n$-manifold admitting a quarter-symmetric metric connection (QSMC). In addition, we developed the characterization of CERYS on $M$-projectively flat, $Q$-flat, and concircularly flat anti-invariant submanifolds of a $(LCS)_n$-manifold with respect to the aforementioned connection. Finally, we construct an example that appoints some of our inference.

Keywords

Conformal $\eta$-Ricci-Yamabe soliton, submanifolds of a (LCS)n -manifolds, quarter symmetric metric connection, M-projectively flat, pseudo-projectively flat, Q-flat.

Ethical Statement

I have declaim that there is no any ethical issue

Supporting Institution

NA

Project Number

NA

Thanks

NA

References

• Atceken, M., Hui, S. K., Slant and pseudo-slant submanifolds in $(LCS)_n$-manifolds, Czechoslovak Math. J., 63 (2013), 177-190. http://eudml.org/doc/252505
• Basu, N., Bhattacharyya, A., Conformal Ricci soliton in Kenmotsu manifold. Global Journal of Advanced Research on Classical and Modern Geometries, 4 (2015), 15-21.
• Baishya, K. K., Eyasmin, S., Generalized weakly Ricci-symmetric $(LCS)_n$-Spacetimes, J. of Geom. and Physics, 132 (2018), 415-422. https://doi.org/10.1016/j.geomphys.2018.05.029
• De, U. C., Sardar, A., De, K., Ricci-Yamabe solitons and 3-dimensional Riemannian manifolds, Turk J. of Math., 6(3) (2022), 1078-1088. https://doi.org/10.55730/1300-0098.3143
• De, U. C., Haseeb, A., On generalized Sasakian space forms with $M$-projective curvature tensor, Adv. Pure Appl. Math., 9 (2018), 67-73. https://doi.org/10.1515/apam-2017-0041
• Fischer, A. E., An introduction to conformal Ricci flow, Classical and Quantum Gravity, 21 (2004), 171-218. https://doi.org/10.1088/0264-9381/21/3/011
• Güler, S., Crasmareanu, M., Ricci-Yamabe maps for Riemannian flows and their volume variation and volume entropy, Turk J. Math., 43 (2019), 2631-2641. https://doi.org/10.3906/mat-1902-38
• Golab, S., On semi-symmetric and quarter symmetric linear connections, Tensor (N.S.), 29 (1975), 249-254.
• Prasad, R., Haseeb, A., On a Lorentzian para-Sasakian manifold with respect to the quarter symmetric-metric connection, Novi Sad J. Math., 46 (2016), 103-116. https://doi.org/10.30755/NSJOM.04279
• Hui, S. K. Pal, T., Totally real submanifolds of $(LCS)_n$-manifolds, Facta Universitatis (NIS) Ser. Math. Inform., 33 (2018.), 141-152. https://doi.org/10.22190/FUMI1802141H
• Hui, S. K., Prasad, R., Pal, T., Ricci solitons on submanifolds of $(LCS)_n$-manifolds, Ganita, 68 (2018), 53-63. https://doi.org/10.48550/arXiv.1707.06815
• Ahmad, M., Jun, J. B., Haseeb, A., Hypersurfaces of an almost r-paracontact Riemannian manifold endowed with a quarter symmetric metric connection, Bull. Korean Math. Soc., 46 (2009), 477-487. https://doi.org/10.4134/BKMS.2009.46.3.477
• Matsumoto, K., On Lorentzian almost paracontact manifolds, Bull. of Yamagata Univ. Nat. Sci., 12(1989), 151-156.
• Mihai, I., Rosca, R., On Lorentzian para-Sasakian manifolds, Classical Analysis, World Scientific Publ. Singapore, 1992.
• Mantica, C. A., Suh, Y. J., Pseudo-$Q$-symmetric Riemannian manifolds, International Journal of Geometric Methods in Modern Physics, 10 (2013), 25 pages. https://doi.org/10.1142/S0219887813500138
• Yadav, S. K., Yildiz, A., $Q$-curvature tensor on $f$-Kenmotsu 3-manifolds, Universal Journal of Mathematics and Applications, 5(3) (2022), 96-106. https://doi.org/10.32323/ujma.1055272
• Yadav, S. K., Dwivedi, P. K., Suthar, D. L., On $(LCS)_{2n+1}$-manifolds satisfying certain conditions on the concircular curvature tensor, Thai J. Math., 9(3) (2011), 597-603.
• Mantica, C. A., Molinari, L. G., A note on concircular structure space-times, Commun. Korean Math. Soc., 34(2) (2019), 633-635. https://doi.org/10.4134/CKMS.c180138
• Maksimovic, M. D., Zlatanovic., M. L., Quarter-symmetric metric connection on a cosymplectic manifold, Mathematics, 11(9) (2023), 2209. https://doi.org/10.3390/math11092209
• Pokhariyal, G. P., Mishra, R. S., Curvature tensors and their relativistic significance II, Yokohama Math. J., 19(2) (1971), 97-103. http://hdl.handle.net/11295/38452
• Prasad, B., A pseudo-projective curvature tensor on a Riemannian manifold, Bull. Calcutta Math. Soc., 94(3) (2002), 163-166.
• Shaikh, A. A., On Lorentzian almost paracontact manifolds with a structure of the concircular type, Kyungpook Math. J., 43 (2003), 305-314.
• Shaikh, A. A., Matsuyama, Y., Hui, S. K., On invariant submanifolds of $(LCS)_n$-manifolds, Journal of the Egyptian Mathematical Society, 24 (2016), 263-269. https://doi.org/10.1016/j.joems.2015.05.008
• Shaikh, A. A., Some results on $(LCS)_n$-manifolds, J. Korean Math. Soc., 46 (2009), 449-461. https://doi.org/10.4134/JKMS.2009.46.3.449
• Yano, K., Concircular geometry I, Concircular transformations, Proc. Imp. Acad. Tokyo, 16 (1940), 195-200. https://doi.org/10.3792/PIA/1195579139
• Yano, K., Kon, M., Structures on manifolds, World Scientific publishing, Singapore, 1984. https://doi.org/10.1142/0067
• Yau, S. T., Harmonic functions on complete Riemannian manifolds, Commu. Pure Appl. Math., 28 (1975), 201-228. https://doi.org/10.1002/cpa.3160280203
• Haseeb, A., Khan, M. A., Conformal $\eta$-Ricci-Yamabe solitons within the framework of $\epsilon$-$LP$-Sasakian 3-manifolds, Advances in Mathematical Physics, (2022), Article ID 3847889, 8 pages. https://doi.org/10.1155/2022/3847889
• Haseeb, A., Chaubey, S. K., Khan, M. A., Riemannian 3 manifolds and Ricci-Yamabe Solitons, International Journal of Geometric Methods in Modern Physics, 20(1) (2023): 2350015, 13 pages. https://doig/10.1142/S0219887823500159
• Zhang, P., Li, Y., Roy, S., Dey, S., Bhattacharyya, A., Geometrical structure in a perfect fluid spacetime with conformal Ricci-Yamabe soliton, Symmetry, 14(3) (2022), 594. https://doi.org/10.3390/sym14030594
• Li, Y., Gezer, A., Karakas, E., Some notes on the tangent bundle with a Ricci quarter-symmetric metric connection, AIMS Mathematics, 8(8) (2023), 17335-17353. https://doi.org/10.3934/math.2023886