Normal Paracontact Metric Space Forms Admitting Almost $\eta-$Ricci Solitons

Yıl 2023, Cilt: 11 Sayı: 2, 155 - 161, 31.10.2023

Tuğba Mert , Mehmet Atçeken

Öz

In this paper, we have considered normal paracontact metric space forms admitting almost $\eta-$Ricci solitons in some curvature tensors. Ricci pseudosymmetry concepts of normal paracontact metric space forms admitting $\eta-$Ricci soliton have introduced according to the choosing of some special curvature tensors such as Riemann, concircular, projective and $W_{1}$ curvature tensor$.$ After then, according to the choice of the curvature tensors, necessary conditions are given for normal paracontact metric space form admitting $\eta-$Ricci soliton to be Ricci semisymmetric. Then some characterizations are obtained and some classifications have made under the some conditions.

Anahtar Kelimeler

Ricci-pseudosymmetric Manifold, η-Ricci Soliton, Normal Paracontact Metric Space Form

Kaynakça

• [1] Kenayuki S. and Williams F.L., Almost paracontact and parahodge structures on manifolds, Nagoya Math. J., 99 (1985), 173-187.
• [2] Zamkovoy S., Canonical connections on paracontact manifolds, Ann Glob. Anal. Geom., 36 (2009), 37-60.
• [3] Welyczko J., On Legendre curvaes in 3-dimensional normal almost paracontact metric manifolds, Result. Math., 54 (2009), 377-387.
• [4] Welyczko J., Slant curves in 3-dimensional normal contact metric manifolds, Mediterr. J. Math., 11 (2014), 965-978.
• [5] Pandey H.B. and Kumar A., Anti invariant submanifolds of almost paracontact metric manifolds, Indian J. pure appl. math., 16(6) (1985), 586-590.
• [6] Yıldırım U¨ ., Atc¸eken M. and Dirik S., A normal paracontact metric manifold satisfying some conditions on the M􀀀projectivecurvature tensor, Konuralp Journal of Mathematics, 7(1) (2019), 217-221.
• [7] Yıldırım U¨ ., Atc¸eken M. and Dirik S., Pseudo projective curvture tensor satisfying some properties on a normal paracontactmetric manifold, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(1) (2019), 997-1006.
• [8] Perelman G., The entropy formula for the Ricci flow and its geometric applications,http://arXiv.org/abs/math/0211159, (2002), 1–39.
• [9] Perelman G., Ricci flow with surgery on three manifolds, http://arXiv.org/abs/math/0303109, (2003), 1–22.
• [10] Sharma R., Certain results on k-contact and (k;m)􀀀contact manifolds, J. Geom., 89 (2008),138–147.
• [11] Ashoka S.R, Bagewadi C.S. and Ingalahalli G., Certain results on Ricci Solitons in a􀀀Sasakian manifolds, Hindawi Publ. Corporation, Geometry, Vol.(2013), Article ID 573925,4 Pages.
• [12] Ashoka S.R., Bagewadi C.S. and Ingalahalli G., A geometry on Ricci solitons in (LCS)n􀀀manifolds, Diff. Geom.-Dynamical Systems, 16 (2014), 50–62.
• [13] Bagewadi C.S. and Ingalahalli G., Ricci solitons in Lorentzian-Sasakian manifolds, Acta Math. Acad. Paeda. Nyire., 28 (2012), 59-68.
• [14] Ingalahalli G. and Bagewadi C.S., Ricci solitons in a􀀀Sasakian manifolds, ISRN Geometry,Vol.(2012), Article ID 421384, 13 Pages.
• [15] Bejan C.L. and Crasmareanu M., Ricci Solitons in manifolds with quasi-contact curvature, Publ. Math. Debrecen, 78 (2011), 235-243.
• [16] Blaga A.M., h􀀀Ricci solitons on para-kenmotsu manifolds, Balkan J. Geom. Appl., 20 (2015), 1–13.
• [17] Chandra S., Hui S.K. and Shaikh A.A., Second order parallel tensors and Ricci solitons on (LCS)n-manifolds, Commun. Korean Math. Soc., 30 (2015), 123–130.
• [18] Chen B.Y. and Deshmukh S., Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl., 19 (2014), 13–21.
• [19] Deshmukh S., Al-Sodais H. and Alodan H., A note on Ricci solitons, Balkan J. Geom. Appl.,16 (2011), 48–55.
• [20] He C. and Zhu M., Ricci solitons on Sasakian manifolds, arxiv:1109.4407V2, [Math DG], (2011).
• [21] Atc¸eken M., Mert T. and Uygun P., Ricci-Pseudosymmetric (LCS)n􀀀manifolds admitting almost h􀀀Ricci solitons, Asian Journal of Math. and Computer Research, 29(2), 23-32,2022.
• [22] Nagaraja H. and Premalatta C.R., Ricci solitons in Kenmotsu manifolds, J. Math. Analysis, 3(2) (2012), 18–24.
• [23] Tripathi M.M., Ricci solitons in contact metric manifolds, arxiv:0801,4221 V1, [Math DG], (2008).
• [24] Ayar G. and Yıldırım M., h􀀀Ricci solitons on nearly Kenmotsu manifolds, Asian-European Journal of Mathematics 12(6) (2019).
• [25] Ayar G. and Yıldırım M., Ricci solitons and gradient Ricci solitons on nearly Kenmotsu manifolds, Facta Unıversitatis(Nis)Ser.Math.Inform.,34 (2019), 503-510.
• [26] Yıldırım M. and Ayar G.,Ricci solitons and gradient Ricci solitons on nearly cosyplectic manifolds, Journal of Universal Mathematics, 4(2) (2021), 201-208.
• [27] Ayar G. and Demirhan D., Ricci Solitons on Nearly Kenmotsu Manifolds with Semi-symmetric Metric Connection, Journal of Engineering Technology and Applied Sciences, 4(3) (2019), 131-140.
• [28] Cho J.T. and Kimura M., Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J. 61(2) (2009), 205-212.