Korean J. Math. Vol. 28 No. 4 (2020) pp.803-817
DOI: https://doi.org/10.11568/kjm.2020.28.4.803

$\eta $-Ricci solitons on Kenmotsu manifolds admitting general connection

Main Article Content

Ashis Biswas
Ashoke Das
Kanak Kanti Baishya
Manoj Ray Bakshi


The object of the present paper is to study $\eta $-Ricci soliton on Kenmotsu manifold with respect to general connection.

Article Details


[1] A. Ba ̧sari, C. Murathan, On generalised φ- reccurent Kenmotsu manifolds, SDU Fen Dergisi 3 (1) (2008), 91–97. Google Scholar

[2] K. K. Baishya & P. R. Chowdhury, On generalized quasi-conformal N(k,μ)-manifolds, Commun. Korean Math. Soc., 31 (1) (2016), 163–176. Google Scholar

[3] A. Biswas and K.K. Baishya, Study on generalized pseudo (Ricci) symmetric Sasakian manifold admitting general connection, Bulletin of the Transilvania University of Brasov, 12 (2) (2019), https://doi.org/10.31926/but.mif.2019. Google Scholar

[4] A. Biswas and K.K. Baishya, A general connection on Sasakian manifolds and the case of almost pseudo symmetric Sasakian manifolds, Scientific Studies and Research Series Mathematics and Informatics, 29 (1) (2019). Google Scholar

[5] A. Biswas, S. Das and K.K. Baishya,On Sasakian manifolds satisfying curvature restrictions with respect to quarter symmetric metric connection, Scientific Studies and Research Series Mathematics and Informatics, 28 (1) (2018), 29–40. Google Scholar

[6] D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, Boston, 2002. Google Scholar

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

[8] K.Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, Princeton University Press,32 (1953). Google Scholar

[9] K. K. Baishya and P. R. Chowdhury, η-Ricci solitons in (LCS)n-manifolds, Bull. Transilv. Univ. Brasov, 58 (2) (2016), 1–12. Google Scholar

[10] L. P.Eisenhart, Riemannian Geometry, Princeton University Press, (1949). Google Scholar

[11] Golab, S., On semi-symmetric and quarter-symmetric linear connections, Tensor(N.S.) 29 (1975), 249–254. Google Scholar

[12] Y.Ishii, On conharmonic transformations, Tensor (N.S.),7 (1957), 73–80. Google Scholar

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

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

[15] K. K. Baishya, More on η-Ricci solitons in (LCS)n-manifolds, Bulletin of the Transilvania University of Brasov, Series III, Maths, Informatics, Physics., 60 (1), (2018), 1–10 Google Scholar

[16] K. K. Baishya, Ricci Solitons in Sasakian manifold, Afr. Mat. 28 (2017), 1061- 1066, DOI: 10.1007/s13370-017-0502-z. Google Scholar

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

[18] D. G. Prakasha and B. S. Hadimani, η-Ricci solitons on para-Sasakian manifolds, J. Geom. 108 (2017), 383–392. Google Scholar

[19] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, http://arXiv.org/abs/math/0211159, (2002), 1–39. Google Scholar

[20] G. Perelman, Ricci flow with surgery on three manifolds, http://arXiv.org/abs/math/0303109, (2003), 1–22. Google Scholar

[21] G.P. Pokhariyal and R.S. Mishra, Curvature tensors and their relativistic significance, Yokohama Math. J. 18 (1970), 105–108. Google Scholar

[22] G.P. Pokhariyal and R.S. Mishra, Curvature tensors and their relativistic significance II, Yokohama Math. J. 19 (2) (1971), 97–103. Google Scholar

[23] R. Sharma, Certain results on κ-contact and ( κ,μ)-contact manifolds, J. Geom. 89 (2008), 138–147. Google Scholar

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

[25] S. Deshmukh, H. Alodan and H. Al-Sodais, A note on Ricci solitons, Balkan J. Geom. Appl. 16 (2011), 48–55. Google Scholar

[26] Schouten, J. A. and Van Kampen, E. R., Zur Einbettungs-und Krummungs theorie nichtholonomer, Gebilde Math. Ann. 103 (1930), 752–783. Google Scholar

[27] S. M. Webster, h Pseudo hermitian structures on a real hypersurface, J. Differ. Geom. 13 (1978), 25–41. Google Scholar

[28] S. Eyasmin, P. Roy Chowdhury and K. K. Baishya, η-Ricci solitons in Kenmotsu manifolds, Honam Mathematical J 40 (2) (2018), 383–392. Google Scholar

[29] S. Tanno, The automorphism groups of almost contact Riemannian manifold, Tohoku Math. J. 21 (1969), 21–38. Google Scholar

[30] V. F. Kirichenko, On the geometry of Kenmotsu manifolds , Dokl. Akad. Nauk, Ross. Akad. Nauk 380 (2001), 585–587. Google Scholar

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

[32] Yano, K., On semi-symmetric connection. Revue Roumanie de Mathematiques Pures et appliquees, 15(1970), 1579–1586. Google Scholar

[33] S. Zamkovoy, Canonical connections on paracontact manifolds. Ann. Global Anal. Geom. 36 (1) (2008), 37–60. Google Scholar