η-Ricci solitons in a LP-Sasakian manifolds admitting quarter-symmetric metric connection

Abhishek Singh, Sangeeta Gautam, Lalit Kumar

Abstract


The objective of this paper is to investigate the $\eta$-Ricci solitons in a LP-Sasakian manifolds admitting quarter-symmetric metric connection satisfying certain curvature conditions. We study the Ricci solitons in a LP-Sasakian manifolds admitting quarter-symmetric metric connection satisfying certain conditions. Finally, we have given an example of 3-dimensional $\eta$-Ricci solitons in a LP-Sasakian manifolds with respect to quarter-symmetric metric connection.

Keywords


LP-Sasakian manifolds, Quarter-symmetric metric connection, $\eta$-Ricci solitons, Second order parallel tensor, $\eta$-Einstein manifold.

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References


Ashoka, S. R., Bagewadi, C. S., Ingalahalli, G., A geometry on Ricci solitons in (LCS) n-manifolds, Diff. Geom. Dynamical Systems, 16 (2014), 50–62.

Aqeel, A. A., De, U. C., Ghosh, G. C., On Lorentzian Para-Sasakian manifolds, Kuwait J. Sci. Eng., 31(2) (2004), 1–13.

Ali, M., Ahsan, Z., Gravitational field of Schwarzschild soliton, Arab J. Math. Sci., 21 (2015), 15–21.

Bagewadi, C. S., Ingalahalli, G., Ashoka, S. R., A study on Ricci solitons in Kenmotsu manifolds, ISRN Geometry, (2013), Article ID 422593, 6 pages.

Bagewadi, C. S., Ingalahalli, G., Ricci solitons in Lorentzian α-Sasakian manifolds, Acta Math. Acad. P. N., 28 (2012), 59–68.

Bejan, C. L., Crasmareanu, M., Ricci solitons in manifolds with Quasi-contact curvature, Publ. Math. Debrecen, 78(1) (2011), 235–243.

Blaga, A. M., η-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl., 20 (2015), 1–13.

Blaga, A. M., η-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30(2) (2016), 489–496.

Chandra, S., Hui, S. K., Shaikh, A. A., Second order parallel tensors and Ricci solitons on (LCS) n -manifolds, Commun. Korean Math. Soc., 30 (2015), 123–130.

Chen, B. Y., Deshmukh, S., Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl., 19 (2014), 13–31.

Cho, J. T., Kimura, M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., 61(2) (2009), 205–212.

De, U. C., Mondal, A. K., Quarter-symmetric metric connection on 3-dimensional quasi-Sasakian manifolds, SUT J. Math., 46 (2010), 35–52.

Golab, S., On Semi-symmetric and quarter-symmetric linear connections, Tensor N. S., 29 (1975), 249–254.

He, C., Zhu, M., Ricci solitons on Sasakian manifolds, (2011), arXiv:1109.4407v2 [math.DG].

Hamilton, R. S., The Ricci flow on surfaces, mathematics and general relativity, Contemp. Math., 71 (1988), 237–262. https://doi.org/10.1090/conm/071/95441

Haseeb, A., Prasad, R., On a Lorentzian Para-Sasakian manifolds with respect to quarter symmetric metric connection, Novi Sad J. Math., 46(2) (2016), 103–116. https://doi.org/10.30755/NSJOM.04279

Haseeb, A., Prasad, R., η-Ricci solitons on ϵ-Lorentzian para-Sasakian manifolds with a quarter-symmetric metric connection, Honam Mathematical J., 41(3) (2019), 539–558. https://doi.org/10.5831/HMJ.2019.41.3.539

Matsumoto, K., On Lorentzian para contact manifolds, Bulletin of Yamagata University, Natural Science, 12(2) (1989), 151–156.

Mihai, I., Rosca, R., On Lorentzian P-Sasakian manifolds, Classical Analysis, World Scientific, Singapore (1992), 155–169.

Mishra, R. S., Pandey, S. N., On quarter-symmetric metric F-connections, Tensor N. S., 34 (1980), 1–7.

Mandal, K., De, U. C., Quarter-symmetric metric connection in a P-Sasakian manifold, Analele Univ. de Vest, Timișoara Seria Matematica-Informatica, LIII(1) (2015), 137–150.

Nagaraja, H. G., Premalatha, C. R., Ricci solitons in Kenmotsu manifolds, Journal of Mathematical Analysis, 3 (2012), 18–24.

Prakasha, D. G., Hadimani, B. S., η-Ricci solitons on para-Sasakian manifolds, J. Geom., 108(2) (2017), 383–392.

Prasad, R., Haseeb, A., Conformal curvature tensor on K-contact manifolds with respect to the quarter-symmetric metric connection, Facta Universitatis (Niš), Ser. Math. Inform., 32 (2017), 503–514.

Rastogi, S. C., On quarter-symmetric metric connections, Tensor, 44 (1987), 133–141.

Rastogi, S. C., On quarter-symmetric metric connection, C. R. Acad. Sci. Bulgar., 31 (1978), 811–814.

Singh, A., Kumar, L., Yadav, S. K., W8-curvature tensor on ϵ-LP-Sasakian manifold, Journal of Rajasthan Academy of Physical Sciences, 22(3–4) (2023), 279–288. https://raops.org.in

Singh, A., Kishor, S., Pankaj, Kumar, L., Characterization of the Lorentzian Para-Sasakian manifolds admitting a new type of semi-symmetric non-metric connection, Ganita, 73(2) (2023), 149–163.

Singh, R. N., Pandey, S. K., On quarter-symmetric metric connection in a LP-Sasakian manifold, Thai J. Math., 12 (2014), 357–371.

Singh, A., Kishor, S., Some type of η-Ricci solitons on Lorentzian para-Sasakian manifolds, Facta Universitatis (Niš), 33(2) (2018), 217–230.

Turan, M., Yetim, C., Chaubey, S. K., On quasi Sasakian 3-manifolds admitting η-Ricci solitons, Filomat, 33(15) (2019), 4923–4930.

Yano, K., Imai, T., Quarter-symmetric metric connections and their curvature tensors, Tensor N. S., 38 (1982), 13–18.




DOI: http://dx.doi.org/10.23755/rm.v54i0.1632

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