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

Ashis Biswas, Ashoke Das, Kanak Kanti Baishya, Manoj Ray Bakshi

Abstract


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

Keywords


quarter symmetric metric connection, Schouten-Van Kampen connection, Tanaka Webster connection, Zamkovoy connection, general connection.

Subject classification

53C15, 53C25

Sponsor(s)



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References


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

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)

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.2019.12.61.2.4. (Google Scholar)

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)

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)

D. E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Birkhauser, Boston, 2002. (Google Scholar)

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

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

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)

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

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

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

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)

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

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)

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

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)

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

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

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

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

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

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

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

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

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

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

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)

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

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

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

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

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


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