Acknowledgement
The authors are thankful to the referees for their valuable suggestions towards to the improvement of the paper.
References
- D. E. Blair, T. Koufogiorgos, and B. J. Papantoniou, Contact metric manifolds satisfying a nulitty condition, Israel. J. Math., 91 (1995), 189-214. https://doi.org/10.1007/BF02761646
- D. E. Blair, Contact Manifolds in Reimannian Geometry, Lecture Notes in Mathematics 509, Springer-Verlag, Berlin, (1976).
- D. E. Blair, Reimannian Geometry of Contact and Sympletic Manifolds, Progress in Mathematics 203, Birkhauser, Basel, (2010).
- K. K. Baishya and P. R. Chowdhury, On generalized quasi-conformal N(κ, µ)-manifolds, Commun. Korean Math. Soc.,31 (2016), 163-176. https://doi.org/10.4134/CKMS.2016.31.1.163
- W. G. Boskoff, M. Crasmareanu and L. I. Piscoran, Tzitzeica equations and Tzitzeica surfaces in separable cordinate systems and the Ricci flow tensor field, Carpathian J. Math., 33(2) (2017), 141-151. https://doi.org/10.37193/CJM.2017.02.01
- J. T. Cho and M. Kimura, Ricci solitons and real hypersurfaces in a complex space-form, Tohoku Math. J., 61 (2009), 205-212. https://doi.org/10.2748/tmj/1245849443
- C. Calin and C. Crasmareanu, From the Eisenhart problem to the Ricci solitons in f-Kenmotau manifolds, Bull. Malays. Math. Sci. Soc., 339(3) (2010), 361-368.
- M. Crasmareanu, New properties of Euclidean Killing tensors of rank two, J. Geom. Symmetry Phys., 51, (2019), 1-7. https://doi.org/10.7546/jgsp-51-2019-1-7
- B. Y. Chen and S. Deshmukh, Geometry of compact shrinking Ricci solitons, Balkan J. Geom. Appl., 19 (2014), 1-12.
- G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds and nullity distributions, J. Geom. 93 (2009), 46-61. https://doi.org/10.1007/s00022-009-1974-2
- G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds with a condition of η-parallelism, Differential Geom. Appl. 27 (2009), 671-679. https://doi.org/10.1016/j.difgeo.2009.03.007
- G. Dileo and A. M. Pastore, Almost Kenmotsu manifolds and local symmetry, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 343-354.
- S. Deshmukh, Jacobi type vector fields on Ricci solitons, Bull. Math. Soc. Sci. Math, Roumanie, 1, 55, 103, (2012), 41-50.
- L. P. Eisenhart,Riemannian Geometry, Princeton University Press,(1949).
- A. Gray, Spaces of constancy of curvature operators, Proc. Amer. Math. Soc., 17 (1966), 897-902. https://doi.org/10.1090/S0002-9939-1966-0198392-4
- R. S. Hamilton The Ricci flow on surfaces, Contemporary Mathematics, 71 (1988), 237-262. https://doi.org/10.1090/conm/071/954419
- S. K. Hui, S. K. Yadav and S. K. Chaubey, η-Ricci soliton on 3-dimensional f-Kenmotsu manifolds, An International Journal, Applications and Applied Mathematics, 13, 2, (2018), 933-951.
- S. K. Hui and D. Chakraborty, Generalized Sasakian-space-forms and Ricci almost solitons with a conformal Killing vector field, New Trends in Math. Sciences, 4 (2016), 263-269. https://doi.org/10.20852/ntmsci.2016320381
- S. K. Hui and D. Chakraborty, Para-Sasakian manifolds and Ricci solitons, Ilirias J. of Math., 6 (2017), 25-34.
- S. K. Hui and D. Chakraborty, Ricci almost solitons on Concircular Ricci pseudosymmetric β-Kenmotsu manifolds, Hacettepe Journal of Mathematics and Statistics, 47(3) (2018), 579-587.
- S. K. Hui and A. Patra, Ricci almost solitons on Riemannian manifolds, Tamsui Oxford J. Information and Mathematical Sciences, 31(2) (2017), 1-8.
- S. K. Hui, R. Prasad and D. Chakraborty, Ricci solitons on Kenmotsu manifolds with respect to quarter symmetric non-metric ϕ-connection, Ganita, 67 (2017), 195-204.
- S. K. Hui, S. Uddin and D. Chakraborty, Generalized Sasakian-space-forms whose metric is η-Ricci almost solitons, Differential Geometry and Dynamical Systems, 19 (2017), 45-55.
- S. K. Hui, S. K. Yadav and A. Patra, Almost conformal Ricci solitons on f-Kenmotsu manifolds, Khayyam J. Math., 5 (2019), 84-104.
- Y. Ishii, On conharmonic transformations, Tensor, N. S., 7 (1957), 73-80.
- T. Ivey, Ricci solitons on compact 3-manifolds, Different. Geom. Appl., 3 (1993), 301-307. https://doi.org/10.1016/0926-2245(93)90008-O
- K. Kenmotsu, A class of almost contact Riemannian manifolds, Tohoku Mathematical Journal 24, 1 (1972), 93-103. https://doi.org/10.2748/tmj/1178241594
- A. M. Pastore and V. Saltarelli, Almost Kenmotsu manifolds with conformal Reeb foliation, Bull. Belg. Math. Soc. Simon Stevin, 21 (2012), 343-354.
- A. M. Pastore and V. Saltarelli, Generalized nullity distribution on an almost Kenmotsu manifolds, J. Geom., 4 (2011), 168-183.
- G. P. Pokhariyal and R. S. Mishra, Curvature tensor and their relativistic significance II, Yokohama Math. J.,19 (1971), 97-103.
- S. Tanno, Some differential equation on Reimannian manifolds, J. Math. Soc. Japan 30 (1978), 509-531. https://doi.org/10.2969/jmsj/03030509
- Y. Wang and X. Liu, Remannian semisymmetric almost Kenmotsu manifolds and nullity distributions, Ann. Polon. Math. 112 (2014), 37-46. https://doi.org/10.4064/ap112-1-3
- Y. Wang and X. Liu, On ϕ-recurrent almost kenmotsu manifolds, Kuwait J. Sci., 42 (2015), 65-77.
- Y. Wang and X. Liu, Second order parrallel tensors on almost Kenmotsu manifolds satisfying the nullity distributions, Filomat, 28 (2014), 839-847. https://doi.org/10.2298/FIL1404839W
- K. Yano and S. Sawaki, Riemannian manifolds admitting a conformal transformation group, J. Diff. Geom., 2 (1968), 161-184.
- K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Math Studies 32, Princeton University Press, (1953).
- S. K. Yadav and M. D. Sidhiqui, On Almost Kenmotsu (κ, µ, ν)-spaces, Differential Geometry - Dynamical Systems, 23, (2021), 263-282.
- S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain geometric properties of η-Ricci soliton on η-Einstein para-Kenmotsu manifolds, Palestine Journal of Mathematics, 9, 1, (2020), 237-244.
- S. K. Yadav, A. Kushwaha and D. Narain, Certain results for η-Ricci soliton and Yamabe soliton on quasi-Sasakian 3-manifolds, Cubo A mathematical Journal, 21, 2, (2019), 77-98. https://doi.org/10.4067/S0719-06462019000200077
- Sunil Kumar Yadav, Ricci solitons on para-Kaehler manifolds, Extracta Mathematikae, 34,2, (2019), 269-284.
- S. K. Yadav, S. K.Chaubey and D. L. Suthar, Some results of η-Ricci soliton on (LCS)n-manifolds, Surveys in Mathematics and its Applications, 13, (2018), 237-250.
- S. K. Yadav, S. K. Chaubey and D. L. Suthar, Certain results on Almost Kenmotsu (κ, µ, ν)-spaces, Konuralp Journal of Mathematics, 6, 1, (2018), 128-133.
- S. K. Yadav, S. K. Chaubey and D. L . Suthar, Some geometric properties of η-Ricci soliton and gradient Ricci soliton on (LCS)2n+1-manifolds, Cubo A Mathematical Journal, 19, 2, (2017), 33-48. https://doi.org/10.4067/S0719-06462017000200033