Some Curvature Conditions on 3-Dimensional Quasi-Sasakian Manifolds Admitting Conformal Ricci Soliton

Year 2023, Volume: 15 Issue: 2, 375 - 381, 31.12.2023

Müslüm Aykut Akgün , Bilal Eftal Acet

https://doi.org/10.47000/tjmcs.1082849

Cited By: 1

Abstract

In this paper, we examine 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton. We give some theorems for $W_{0}^{*}$ flat, $\xi-W_{0}^{*}$ flat and $\phi-W_{0}^{*}$ semisymmetric 3-dimensional quasi-Sasakian manifold admitting conformal Ricci soliton. Also we study conformal Ricci soliton on a 3-dimensional quasi-Sasakian manifold satisfying the conditions $W_{0}^{*}(\xi,X).S=0$ and $R(\xi,X).W_{0}^{*}=0$.

Keywords

Ricci soliton , conformal Ricci soliton , quasi-Sasakian manifold.

References

• Basu, N., Bhattacharyya A., Conformal Ricci soliton in Kenmotsu manifold, Glob. J. of Adv. Research on Class. Modern Geom., 4(1)(2015), 15–21.
• Blaga, M.A.,η−Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30(2)(2016), 489–496.
• Blaga, M.A., Y¨uksel Perktas¸, S., Erdo˘gan, F.E., Acet, B.E., η−Ricci solitons in (ε)−almost paracontact metric manifolds, Glasnik Math., 53(1)(2018), 205–220.
• Blair, D.E., The theory of quasi-Sasakian structures, J. Diff Geo., 1(1967), 331–345.
• Calin, C., Crasmareanu, M., From the Eisenhart problem to Ricci solitons in f−Kenmotsu manifolds, Bull. Malays. Math. Sci. Soc., 33(3)(2010), 361–368.
• 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., Majhi P., φ−semisymmetric generalized Sasakian space-forms, Arab J. Math. Sci., 21(2)(2015), 170–178.
• De, U.C., Mondal, A.K., 3-dimensional quasi-Sasakian manifolds and Ricci solitons, SUT J. Math., 48(1)(2012), 71–81.
• De, U.C., Sarkar, A., On three-dimensional quasi-Sasakian manifolds, SUT J. Math., 45(1) 2009), 59–71.
• De, U.C., Yildiz, A., Turan, M., Acet, B. E., 3-dimensional quasi-Sasakian manifolds with semi-symmetric non-metric connection, Hacettepe J. Math. Stat., 41(1)(2012), 127–137.
• De, U.C., De, K., Khan, M.N.I., Almost co-K¨ahler manifolds and quasi-Einstein solitons, Chaos, Solitons and Fractals, 167(2023).
• Fischer, A.E., An introduction to conformal Ricci flow class, Quantum Grav., 21(3)(2004), 171–218.
• Gautam, U.K., Haseeb, A., Prasad R., Some results on projective curvature tensor in Sasakian manifolds, Commun. Korean Math. Soc., 34(3)(2019), 881–896.
• Ghosh, S., η−Ricci solitons on quasi-Sasakian manifolds, An. Univ. Vest Timi¸s. Ser. Mat.-Inform., 56(1)(2018), 73–85.
• Gonzalez, J.C., Chinea, D., Quasi-Sasakian homogeneous structures on the generalized Heisenberg group H(p, 1), Proc. Amer. Math. Soc., 105(1)(1989), 173–184.
• Haseeb, A., Prasad, R., η−Ricci solitons on ε−LP-Sasakian manifolds with a quartersymmetric metric connection, Honam Math. J., 41(3)(2019), 539–558.
• Haseeb, A., Bilal, M., Chaubey, S.K., Khan, M.N.I., Geometry of indefinite Kenmotsu manifolds as ∗η-Ricci-Yamabe solitons, Axioms, 11(9)(2022), 461.
• Kanemaki, S., Quasi-Sasakian manifolds, Tohoku Math. J., 29(2)(1977), 227–233.
• Kanemaki, S., On Quasi-Sasakian manifolds in Differential Geometry, Banach Center Publ., Warsaw, 1979.
• Majhi, P., De, U.C., Kar, D., η−Ricci solitons on Sasakian 3-manifolds, An. Univ. Vest Timis. Ser. Mat.-Inform., 55(2)(2017), 143–156.
• Olszak, Z., Normal almost contact metric manifolds of dimension three, Ann. Polon. Math., 47(1)(1986), 41–50.
• Olszak, Z., On three-dimensional conformally flat quasi-Sasakian manifolds, Period. Math. Hungar., 33(2)(1996), 105–113.
• Pokhariyal, G.P., Mishra, R.S., Curvature tensor and their relativistic significance II, Yokohama Math. J., 19(2)(1971), 97–103.
• Prakasha, D.G., Hadimani, B.S., η−Ricci solitons on para-Sasakian manifolds, J. Geom., 108(2)(2017), 383–392.
• Sardar, A., Khan, M.N.I., De, U.C., h-*-Ricci solitons and almost co-K¨ahler manifolds, Mathematics, 9(24)(2021), 3200.
• Turan, M., Yetim, C., Chaubey, S.K., On quasi-Sasakian 3-manifolds admitting η−Ricci solitons, Filomat, 33(15)(2019), 4923–4930.
• Walker, A.G., On Ruse’s spaces of recurrent curvature, Proc. London Math. Soc., 52(2)(1950), 36–64.
• Yano, K., Kon, M., Structures on Manifolds, Series in Pure Mathematics, 3, World Scientific Publishing Co., Singapore, 1984.