Abstract
The object of this paper is to study a special type of metrics called \({\eta}\)-Ricci solitons on para-Sasakian manifolds. We give the existence of para-Sasakian \({\eta}\)-Ricci solitons in our settings. In addition, the non-existence of certain geometric characteristics of para-Sasakian \({\eta}\)-Ricci solitons are studied. Finally, we discuss 3-dimensional and conformally flat para-Sasakian \({\eta}\)-Ricci solitons.
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Bejan, C.L., Crasmareanu, M.: Second order parallel tensors and Ricci solitons in 3-dimensional normal paracontact geometry. Ann. Glob. Anal. Geom. doi:10.1007/s10455-014-9414-4
Blaga A.M.: \({\eta}\)-Ricci solitons on Lorentzian para-Sasakian manifolds. Filomat 30(2), 489–496 (2016)
Blaga A.M.: \({\eta}\)-Ricci solitons on para-Kenmotsu manifolds. Balkan J. Geom. Appl. 20(1), 1–13 (2015)
Blaga, A.M., Crasmareanu, M.C.: Torse-forming η-Ricci solitons in almost paracontact η-Einstein geometry. Filomat (2016, to appear)
Calin C., Crasmareanu M.: Eta-Ricci solitons on Hopf hypersurfaces in complex space forms. Revue Roumaine de Mathematiques pures et appliques 57(1), 55–63 (2012)
Calvaruso, G., Perrone, D.: Geometry of H-paracontact metric manifolds (2013). arXiv:1307.7662v1
Calvaruso G., Zaeim A.: A complete classification of Ricci and Yamabe solitons of non-reductive homogeneous 4-spaces. J. Geom. Phys. 80, 15–25 (2014)
Calvaruso, G., Perrone, A.: Ricci solitons in three-dimensional paracontact geometry (2014). arXiv:1407.3458v1
Cao, H.-D.: Recent progress on Ricci solitons. Adv. Lect. Math. (ALM) 11, 1–38 (2009). arXiv:0908.2006v1
Chaki M.C., Gosh M.L.: On quasi Einstein manifolds. Int. J. Math. 42, 211–220 (2000)
Chen B., Yano K.: Hypersurfaces of a conformally flat space. Tensor N.S. 26, 315–321 (1972)
Cho J.T., Kimura M.: Ricci solitons and real hypersurfaces in a complex space form. Tohoku Math. J. 61(2), 205–212 (2009)
Hamilton, R.S.: The Ricci flow on surfaces. In: Mathematics and general relativity (Santa Cruz, CA, 1986), Contemp. Math., vol. 71, pp. 237–262. Amr. Math. Soc., Providence (1988)
Kaneyuki S., Williams F.L.: Almost paracontact and parahodge structures on manifolds. Nagoya Math. J. 99, 173–187 (1985)
Pina R., Tenenblat K.: On solutions of the Ricci curvature and the Einstein equation. Isr. J. Math., 171, 61–76 (2009)
Prakasha D.G.: Torseforming vector fields in a 3-dimensional para-Sasakian manifold. Sci. Stud. Res. Ser. Math. Inform. 20(2), 61–66 (2010)
Sato I.: On a structure similar to the almost contact structure I. Tensor N.S. 30, 219–224 (1976)
Shukla S.S., Shukla M.K.: On \({\phi}\)-symmetric para-Sasakian manifolds. Int. J Math. Anal. 4(16), 761–769 (2010)
Tarafdar, D., De, U.C.: Second order parallel tensors on P-Sasakian manifolds. Northeast. Math. J., 11(3), 260–262 (1995)
Takahashi T.: Sasakian manifold with pseudo-Riemannian metric. Tohoku Math. J. 21(2), 644–653 (1969)
Yano, K., Kon, M.: Structures on manifolds. Series in Pure Mathematics, vol. 3. World Scientific, Singapore (1984)
Zamkovoy S.: Canonical connections on paracontact manifolds. Ann Glob Anal Geom. 36(1), 37–60 (2009)
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Prakasha, D.G., Hadimani, B.S. \({\eta}\)-Ricci solitons on para-Sasakian manifolds. J. Geom. 108, 383–392 (2017). https://doi.org/10.1007/s00022-016-0345-z
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DOI: https://doi.org/10.1007/s00022-016-0345-z