Browse > Article
http://dx.doi.org/10.5831/HMJ.2020.42.3.601

η-RICCI SOLITONS ON TRANS-SASAKIAN MANIFOLDS WITH QUARTER-SYMMETRIC NON-METRIC CONNECTION  

Bahadir, Oguzhan (Department of Mathematics, Faculty of Science and Letters, Kahramanmaras Sutcu Imam University)
Siddiqi, Mohd Danish (Department of Mathematics Faculty of Science, Jazan University)
Akyol, Mehmet Akif (Department of Mathematics, Faculty of Arts and Sciences, Bingol University)
Publication Information
Honam Mathematical Journal / v.42, no.3, 2020 , pp. 601-620 More about this Journal
Abstract
In this paper, firstly we discuss some basic axioms of trans Sasakian manifolds. Later, the trans-Sasakian manifold with quarter symmetric non-metric connection are studied and its curvature tensor and Ricci tensor are calculated. Also, we study the η-Ricci solitons on a Trans-Sasakian Manifolds with quartersymmetric non-metric connection. Indeed, we investigated that the Ricci and η-Ricci solitons with quarter-symmetric non-metric connection satisfying the conditions ${\tilde{R}}.{\tilde{S}}$ = 0. In a particular case, when the potential vector field ξ of the η-Ricci soliton is of gradient type ξ = grad(ψ), we derive, from the η-Ricci soliton equation, a Laplacian equation satisfied by ψ. Finally, we furnish an example for trans-Sasakian manifolds with quarter-symmetric non-metric connection admitting the η-Ricci solitons.
Keywords
${\eta}-Ricci$ solitons; Trans-Sasakian manifolds; Quarter-symmetric non-metric connection;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 N. S. Agashe and M. R. Chafle, A semi symmetric non-metric connection in a Riemannian manifold, Indian J. Pure Appl. Math. 23 (1992), 399-409.
2 M. Ahmad, J. B. Jun, and M. D. Siddiqi, On some properties of semi-invariant submanifolds of a nearly trans-Sasakian manifolds admitting a quarter-symmetric non-metric connection, Journal of the Chungcheong Math. Soc., 25(1) (2012), 73-90.   DOI
3 A. M. Blaga, ${\eta}$-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat, 30(2) (2016), 489-496.   DOI
4 D. E. Blair, Contact manifold in Riemannian geometry, Lecture Notes in Math., Springer Verlag, 1976.
5 A. Haseeb, M. A. Khan, M. D. Siddiqi, Some more results on an epsilon-Kenmotsu manifold with a semi-symmetric semi-metric connection, Acta Mathematica Universitatis Comenianae, 85(1) (2016), 9-20.
6 J. T. Cho, M. Kimura, Ricci solitons and Real hypersurfaces in a complex space form, Tohoku Math.J., 61 (2009), 205-212.   DOI
7 U. C. De, K. De, On a class of three-dimensional trans-Sasakian manifolds, Commun. Korean Math. Soc., 27(4) (2012), 795-808.   DOI
8 U. C. De, M. M. Tripathi, Ricci tensor in 3-dimensional trans-Sasakian manifolds, Kyungpook Math. J., 2 (2003), 247-255.
9 S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor 29 (1975), 249-254.
10 R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, (Santa Cruz. CA, 1986), Contemp. Math., AMS, 71 (1988), 237-262.   DOI
11 H. A. Hayden, Subspaces of a space with torsion, Proc. London Math. Soc. 34 (1932), 27-50.   DOI
12 D. Janssens, L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J., 4 (1981), 1-27.   DOI
13 J. S. Kim, R. Prasad and M. M. Tripathi, On generalized Ricci-recurrent trans-Sasakian manifolds, J. Korean Math. Soc., 39(6) (2012), 953-961.   DOI
14 J. C. Marrero, , The local structure of trans-Sasakian manifolds, Ann. Mat. Pura Appl., 162(4) (1992), 77-86.   DOI
15 J. A. Oubina, New class of almost contact metric structures, Publ. Math. Debrecen, 32 (1985), 187-193.
16 C. Patra and A. Bhattacharyya, Trans-Sasakian manifold admitting quarter-symmetric non-metric connection, Acta Universitatis Apulensis, 36 (2013), 39-49.
17 S. Sharfuddin and S. I Husain, Semi-symmetric metric connexions in almost contact manifolds, Tensor., 30(1976), 133-139.
18 M. D. Siddiqi, M. Ahmad, and J. P. Ojha, CR-Submanifolds of a nearly trans-hyperbolic Sasakian manifold with a semi-symmetric non-metric connection, African Diaspora Journal of Mathamatics, New Series 17(1) (2014), 93-105.
19 M. D. Siddiqi, ${\eta}$-Ricci Solitons in ${\delta}$-Lorentzian Trans Sasakian Manifolds with a Semi-symmetric metric Connection, Kyungpook Mathematical Journal, 59(3) (2019), 537-562.   DOI
20 M. D. Siddiqi, ${\eta}$-Ricci Solitons in 3-Dimensinonal Normal Almost contact metric manifolds, Bull. of the Transilvania Univ. of Brasov. Math., Informatics, Physics Series III 11(2) (2018), 215-233.
21 M. M. Tripathi, A new connection in a Riemannian manifold, International electronic journal of geometry 1(1)(2008) 15-24.
22 K. Vinu and H.G. Nagaraja, ${\eta}$-Ricci solitons in trans-Sasakian manifolds, Commun. Fac. sci. Univ. Ank. Series A1 66(2) (2017), 218-224.
23 K. Yano and M. Kon Structures on Manifolds, Singapore:World Scientific Publishing co. pte. ltd., (1984).