Korean J. Math. Vol. 29 No. 2 (2021) pp.345-353
DOI: https://doi.org/10.11568/kjm.2021.29.2.345

Riemann solitons on certain type of Kenmotsu manifold

Main Article Content

Manoj Ray Bakshi
Kanak Kanti Baishya
Ashoke Das

Abstract

The object of the present paper is to investigate the nature of Riemannsolitons on generelized $D$-conformally deformed Kenmotsu manifold with hyper generalized pseudo symmetric curvature conditions.


Article Details

References

[1] P. Alegre, D. E. Blair, and A. Carriazo, Generalized Sasakian-space-forms, Israel J. Math. 141 (1) (2004), 157–183. Google Scholar

[2] Google Scholar

[3] K K Baishya, F. Ozen Zengin and J Mike, On hyper generalised weakly symmetric manifolds, Nineteenth International Conference on Geometry, Integrability and Quantization June 02–07, 2017, Varna, Bulgaria Iva ̈ılo M. Mladenov and Akira Yoshioka, Editors Avangard Prima, Sofia 2018, pp 1–10 doi:10.7546/giq-19-2018-1-10 Google Scholar

[4] Google Scholar

[5] K. K. Baishya, P. Peska, and P. R. Chowdhury, On almost generalized weakly symmetric Kenmotsu manifolds, Acta Univ. Palacki. Olomuc., Fac. rer. nat. Mathematica 55 (2) (2016), 5–15. Google Scholar

[6] Google Scholar

[7] M. R. Bakshi and K. K. Baishya, Certain types of (LCS)n -manifolds and the case of Riemann solitons, Differential Geometry-Dynamical Systems 22 (2020),11–25. Google Scholar

[8] Google Scholar

[9] M. R. Bakshi and K. K. Baishya, Four classes of Riemann solitons on alpa-cosymplectic manifolds, Afrika Matematika, https://doi.org/10.1007/s13370-020-00846-6 Google Scholar

[10] Google Scholar

[11] M. R. Bakshi, K. K. Baishya, D. G. Prakasha and P. Veeresha, Ricci solitons in a hyper generalized pseudo symmetric D-homothetically deformed Kenmotsu manifold, submitted Google Scholar

[12] Google Scholar

[13] A. Biswas, A. Das, K. K. Baishya and M. R. Bakshi, η -Ricci solitons on Ken- motsu manifolds admitting General connection, Korean J. Math. 28 (2020) (4), 803–817, http://dx.doi.org/10.11568/kjm.2020.28.4.803 Google Scholar

[14] Google Scholar

[15] A. M. Blaga, M. R. Bakshi, and K. K. Baishya, Hyper generalized pseudo Q-symmetric semi- Riemanian manifold, Cubo, A Mathematical Journal,Vol. 23 (1) (2021), 87–96, Google Scholar

[16] Google Scholar

[17] K. K. Baishya and P. R. Chowdhury, On Generalized Weakly Symmetric Kenmotsu Manifolds, Bol. Soc. Paran. Mat, (3s.) v. 39 6 (2021): 211–222. Google Scholar

[18] A. M. Blaga, K. K. Baishya and N. Sarkar, Ricci solitons in a generalized weakly (Ricci) sym- metric D-homothetically deformed Kenmotsu manifold, Ann. Univ. Paedagog. Crac. Stud. Math. 18 (2019), 123–136 Google Scholar

[19] Google Scholar

[20] D. E. Blair, Contact Manifolds in Riemannian Geometry, Lect. Notes in Math. 509, Springer- Verlag, New York (1976). Google Scholar

[21] Google Scholar

[22] M. C. Chaki, On pseudo symmetric manifolds, Analele Stiintifice ale Universitatii " Al I. Cuza" din Iasi 33 (1987), 53–58. Google Scholar

[23] Google Scholar

[24] R. S. Hamilton, The Ricci flow on surfaces , Contemp. Math. 71 (1988), 237–261. Google Scholar

[25] Google Scholar

[26] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Diff. Geom. 17 (1982), 255– 306. Google Scholar

[27] Google Scholar

[28] K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Math. J. 24 (1972), 93–103 Google Scholar

[29] Google Scholar

[30] Tanno, S., The topology of contact Riemannian manifolds , Illinois J. Math. 12 (1968), 700–717. Google Scholar

[31] Google Scholar

[32] R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, Contemp. Math. 71, American Math. Soc. (1988), 237–262. Google Scholar

[33] Google Scholar

[34] I.E. Hiric ̆a, C. Udriste, Ricci and Riemann solitons , Balkan J. Geom. Applications. 21 (2) (2016), 35–44. Google Scholar

[35] Google Scholar

[36] C. Udri ̧ste, Riemann flow and Riemann wave via bialternate product Riemannian metric. preprint, arXiv.org/math.DG/1112.4279v4 (2012). Google Scholar

[37] Google Scholar

[38] C. Udriste, Riemann flow and Riemann wave, Ann. Univ. Vest, Timisoara. Ser. Mat. Inf. 48 (1-2) (2010), 265–274. Google Scholar

[39] Google Scholar

[40] Nu ̈lifer O ̈zdemir, Sirin Aktay, Mehmet Solgun, On generalized D-conformal deformations of certain almost contact metric manifolds, Mathematics 2019, 0700168. Google Scholar

[41] Google Scholar

[42] Nagaraja, H.G., Kiran Kumar, D.L., Ricci Solitons in Kenmotsu Manifold under Generalized D-Conformal Deformation. Lobachevskii J Math 40 (2019), 195–200. https://doi.org/10.1134/S1995080219020112. Google Scholar

[43] Google Scholar

[44] HG Nagaraja, DL Kiran Kumar, VS Prasad, Ricci solitons on Kenmotsu manifolds under D- homothetic deformation, Khayyam J. Math. 4 (1) (2018), 102–109. Google Scholar

[45] Google Scholar

[46] T. Suguri and S. Nakayama, D-conformal deformations on almost contact metric structure,Tensor (N.S.) 28 (1974), 125–129. Google Scholar

[47] Google Scholar