Acknowledgement
This work does not receive any funding.
References
- B. S. Acharya, A-O'Farrell Figurea, C. M. Hull, and B. J. Spence, Branes at Canonical singularities and holography, Adv. Theor. Math. Phys. 2 (1999), 1249-1286. https://doi.org/10.4310/ATMP.1998.v2.n6.a2
- I. Agricola and T. Friedrich, Killing spinors in super gravity with 4-fluxes, Class. Quant. Grav. 20 (2003), 4707-4717. https://doi.org/10.1088/0264-9381/20/21/010
- S. Azami, Generalized Ricci solitons of three-dimensional Lorentzian Lie groups associated canonical connections and Kobayashi-Nomizu connections, J. Nonlinear Math. Phys. 30 (2023), 1-33.
- A. M. Blaga, Cononical connections on para-Kenmotsu manifolds, Novi Sad J. Math. 45 (2015), no. 2, 131-142. https://doi.org/10.30755/NSJOM.2014.050
- A. M. Blaga, η-Ricci solitons on Lorentzian para-Sasakian manifolds, Filomat 30 (2016), no. 2, 489-496. https://doi.org/10.2298/FIL1602489B
- A. M. Blaga, η-Ricci solitons on para-Kenmotsu manifolds, Balkan J. Geom. Appl. 20 (2015), 1-13.
- A. M. Blaga, Torse-forming η-Ricci solitons in almost paracontact η-Einstein geometry, Filomat,31 (2017), no. 2, 499-504. https://doi.org/10.2298/FIL1702499B
- D. E. Blair, Contact manifolds in Riemannian geometry, Lecture Notes in Mathematics Vol 509. Springer-Verlag, Berlin-New York, 1976.
- D. E. Blair, Riemannian geometry of contact and symplectic manifolds, Progress in Mathematics, Vol. 203. Birkhauser Boston Inc. 2002.
- D. E. Blair, The theory of quasi-Sasakian structure, J. Differential Geo. 1 (1967), 331-345.
- C. Calin and M. Crasmareanu, From the Eisenhart problem to Ricci solitons in f-Kenmotsu manifolds, Bull. Malays. Math. Soc. 33 (2010), no. 3, 361-368.
- G. Calvaruso, Three-dimensional homogeneous generalized Ricci solitons, Mediterr. J. Math. 14 (2017), no. 5, 1-21. https://doi.org/10.1007/s00009-017-1019-2
- T. Chave and G. Valent, Quasi-Einstein metrics and their renormalizability properties, Helv. Phys. Acta. 69 (1996) 344-347.
- T. Chave and G. Valent, On a class of compact and non-compact quasi-Einstein metrics and their renormalizability properties, Nuclear Phys. B. 478 (1996) 758-778. https://doi.org/10.1016/0550-3213(96)00341-0
- B. Y. Chen, Classification of torqued vector fields and its applications to Ricci solitons, Kragujevac J. Math. 41 (2017), no. 2, 239-250. https://doi.org/10.5937/KgJMath1702239C
- B. Y. Chen, A simple characterization of generalized Robertson-Walker space-times, Gen. Relativity Gravitation, 46 (2014), no. 12, Article ID 1833.
- J. T. Cho and M. Kimura, Ricci solitons and real hypersurfaces in a complex space form, Tohoku Math. J. 61 (2009), no. 2, 205-212.
- U. C. De and A. Sarkar,On three-dimensional quasi-Sasakian manifolds, SUT Journal of Mathematics 45 (2009), 59-71.
- U. C. De and A. K. Sengupta, Notes on three-dimensional quasi-Sasakian manifolds, Demonstratio Mathematica XXXVII (3) (2004), 655-660.
- T. Friedrichand and S. Ivanov, Parallel spinors and connections with skew symmetric torsion in string theory, Asian J. Math. 6 (2002), 303-336. https://doi.org/10.4310/AJM.2002.v6.n2.a5
- R. S. Hamilton, The Ricci flow on surfaces, Mathematics and general relativity, Contemp. Math. Santa Cruz, CA, 1986, 71, American Math. Soc. 1988, 237-262. https://doi.org/10.1090/conm/071/954419
- A. Haseeb, S. Pandey, and R. Prasad, Some results on η-Ricci solitons in quasi-Sasakian 3-manifolds, Commun. Korean Math. Soc. 36 (2021), no. 2, 377-387.
- D. Janssens and L. Vanhecke, Almost contact structures and curvature tensors, Kodai Math. J. 4 (1981), no. 1, 1-27.
- P. Majhi, U. C. De, and D. Kar, η-Ricci Solitons on Sasakian 3-Manifolds, Anal. De Vest Timisoara LV (2) (2017), 143-156.
- M. A. Mekki and A. M. Cherif, Generalised Ricci solitons on Sasakian manifolds, Kyungpook Math. J. 57 (2017), 677-682.
- P. Nurowski and M. Randall, Generalized Ricci solitons, J. Geom. Anal. 26 (2016), 1280-1345. https://doi.org/10.1007/s12220-015-9592-8
- Z. Olszak, Normal almost contact metric manifolds of dimension 3, Ann. Polon. Math. 47 (1986), 41-50. https://doi.org/10.4064/ap-47-1-41-50
- Z. Olszak, On three-dimensional conformally flat quasi-Sasakian manifolds, Period. Math. Hungar. 33 (1996), 105-113. https://doi.org/10.1007/BF02093508
- S. Y. Perktas and A. Yildiz, On Quasi-Sasakian 3-manifolds with respect to the Schouten-van- Kampen connection, Int. Electron. J. Geom. 13 (2020), no. 2, 62-67. https://doi.org/10.36890/iejg.742073
- D. G. Prakasha and B. S. Hadimani, η-Ricci solitons on para-Sasakian manifolds, J. Geometry 108 (2017), 383-392. https://doi.org/10.1007/s00022-016-0345-z
- A. Sarkar, A. Sil, and D. Biswas, A study on three-dimensional quasi-Sasakian amnifolds, Indian J. Math. 59 (2017), 209-225.
- A. Sarkary, A. Silz, and A. K. Paul, On three-dimensional quasi-Sasakian, Applied Mathematics E-Notes 19 (2019), 55-64.
- J. A. Schouten, Ricci Calculus, Springer-Verlag, Berlin, 1954.
- M. D. Siddiqi, Generalized η-Ricci solitons in trans Sasakian manifolds, Eurasian bulltein of mathematics 1 (2018), no. 3, 107-116.
- A. F. Solovev, On the curvature of the connection induced on a hyperdistribution in a Riemannian space, Geom. Sb. 19 (1978), 12-23.
- A. F. Solovev, The bending of hyperdistribution, Geom. Sb. 20 (1979), 101-112.
- A. F. Solovev, Second fundemamental form of a distribution, Mat. Zametki 35 (1982), 139-146.
- S. Tanno, Quasi-Sasakian structures of rank 2p + 1, J. Differential Geom. 5 (1971), 317-324. https://doi.org/10.4310/jdg/1214429995
- M. Turana, C. Yetima, and S. K. Chaubey, On quasi-Sasakian 3-manifolds admitting η-Ricci solitons, Filomat 33 (2019), no. 15, 4923-4930. https://doi.org/10.2298/FIL1915923T
- K. Yano, Concircular geometry I. Concircular tranformations, Proc. Imp. Acad. Tokyo 16 (1940), 195-200.
- K. Yano, On the torse-forming directions in Riemannian spaces, Proc. Imp. Acad. Tokyo 20 (1944), 340-345.
- K. Yano and B. Y. Chen, On the concurrent vector fields of immersed manifolds, Kodai Math. Sem. Rep. 23 (1971), no. 3, 343-350.