In this paper, we study η-Ricci solitons on 3-dimensional f-Kenmotsu manifolds with respect to a quarter symmetric metric connection. We obtain some results when the potential vector field is pointwise collinear with the Reeb vector field, conformal Killing vector field and a torqued vector field.
1. M. Altunba¸s, Ricci solitons of three-dimensional Lorentzian Bianchi-Cartan-Vranceanu spaces, Turkish. J. Math. Computer. Sci. 15(2)(2023), 270-276.
2. S. Azami, Generalized η−Ricci soliton son f-Kenmotsu 3-manifolds associated to the Schouten Van Kampen connection, AUT. J. Math. Computing, 5(1)(2024), 18-26.
3. B.Y. Chen, Classification of torqued vector fields and its applications to Ricci solitons, Kragujevac J. Math., 41(2017), 239-250.
4. B.Y. Chen, A simple characterization of generalized RobertsonWalker spacetimes, Gen. Rel. Grav., 46(2014), 1-5.
5. J. T. Cho and M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J., (2)(2009), 205-212.
6. A. Friedmann and J. A. Schouten, Uber die Geometrie der halbsymmetrischen Ubertra- ¨ gung, Math.Zeitschr., 21(1924), 211-223.
7. S. Golab, On semi-symmetric and quarter-symmetric linear connections, Tensor.N.S., 29 (1975), 293-301.
8. R. S. Hamilton, The Ricci flow on surfaces, in Mathematics and general relativity Amer. Math. Soc., Providence, RI, (1988), 237-262.
9. D. Janssens and L. Vanhecke, Almost contact structure and curvature tensor, Kodai Math. J., 4(1981), 1-27.
10. R. S. Mishra and S.N. Pandey, On quarter symmetric metric F-connections, Tensor N.S., 34(1980), 1-7.
11. A. K. Mondal and U.C. De, Some properties of a quarter symmetric connection on a Sasakian manifold, Bull. Math. Annal. and Appl. 3(2009), 99-108.
12. S. Mukhopadyay, A. K. Roy and B. Barua, Some properties of a quarter symmetric metric connection on a Riemannian manifold, Soochow J. Math., 17(1991), 205-211.
13. P. Nurowski and M. Randall, Generalized Ricci solitons, J. Geom. Anal. 26(2016), 1280- 1345.
14. Z. Olszak and R. Rosca, Normal locally conformal almost cosymplectic manifolds, Publ. Math. Debrecen, 39(1991), 315-323.
15. A. Sarkar and N. Biswas, On f-Kenmotsu manifolds and their submanifolds with quarter symmetric metric connections, Facta Ser. Math. Inf. 35(4) (2020), 1017-1030.
16. J. A. Schouten, Ricci-calculus. An introduction to tensor analysis and its geometrical applications, Springer-Verlag, Berlin-G¨ottingen-Heidelberg, 1954. 2d.ed.
17. N.V.C. Shukla and A. Sharma, Study of Ricci solitons in f-Kenmotsu manifolds with the quarter-symmetric metric connection, J˜n¯an¯abha, 53 (1) (2023), 293-299.
18. M. D. Siddiqi, Generalized η−Ricci solitons in trans Sasakian manifolds, Eurasian Bull.Math., 1(2018), 107-116.
19. K. Yano and T. Imai, Quarter symmetric metric connections and their curvature tensors, Tensor N.S., 38 (1982), 13-18.
20. K. Yano, On the torse-forming directions in Riemannian spaces, Proc. Imp. Acad. Tokyo, 20(1944), 340-345.
Altunbaş, M. (2024). Generalized η-Ricci solitons on f -Kenmotsu manifolds admitting a quarter symmetric metric connection. Journal of Finsler Geometry and its Applications, 5(1), 80-87. doi: 10.22098/jfga.2024.14757.1121
MLA
Murat Altunbaş. "Generalized η-Ricci solitons on f -Kenmotsu manifolds admitting a quarter symmetric metric connection", Journal of Finsler Geometry and its Applications, 5, 1, 2024, 80-87. doi: 10.22098/jfga.2024.14757.1121
HARVARD
Altunbaş, M. (2024). 'Generalized η-Ricci solitons on f -Kenmotsu manifolds admitting a quarter symmetric metric connection', Journal of Finsler Geometry and its Applications, 5(1), pp. 80-87. doi: 10.22098/jfga.2024.14757.1121
VANCOUVER
Altunbaş, M. Generalized η-Ricci solitons on f -Kenmotsu manifolds admitting a quarter symmetric metric connection. Journal of Finsler Geometry and its Applications, 2024; 5(1): 80-87. doi: 10.22098/jfga.2024.14757.1121