Abstract
We classify three-dimensional paracontact metric manifold whose Ricci operator Q is invariant along Reeb vector field, that is, \({\mathcal {L}} _{\xi }Q=0\).
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Calvaruso, G.: Homogeneous paracontact metric three-manifolds. Ill. J. Math. 55, 697–718 (2011)
Calvaruso, G., Perrone, D.: H-contact semi-Riemannian manifolds. J. Geom. Phys. 71, 11–21 (2013)
Calvaruso, G., Perrone, D.: Geometry of H-paracontact metric manifolds. Publ. Math. Debrecen 86(3-4), 325–346 (2015)
Calvino-Louzao, E., Seoane-Bascoy, J., Vázquez-Abal, M.E., Vázquez-Lorenzo, R.: Invariant Ricci collineations on three-dimensional Lie groups. J. Geom. Phys. 96, 59–71 (2015)
Cappelletti, Montano B., Küpeli, Erken I., Murathan, C.: Nullity conditions in paracontact geometry. Differ. Geom. Appl. 30, 665–693 (2012)
Cho, J.T.: Contact \(3\)-manifolds with the Reeb flow symmetry. Tohoku Math. J. 66, 491–500 (2014)
Cho, J.T., Kimura, M.: Reeb flow symmetry on almost contact three-manifolds. Differ. Geom. Appl. 35, 266–273 (2014)
Duggal, K.L., Sharma, R.: Symmetries of Spacetimes and Riemannian Manifolds. Kluwer, Dordrecht (1999)
Hall, G.S.: Symmetries and geometry in general relativity. Differ. Geom. Appl. 1, 35–45 (1991)
Küpeli Erken, I., Murathan, C.: A study of three-dimensional paracontact \((\kappa,\mu, v)\)-spaces. Int. J. Geom. Methods Mod. Phys. 14(7), 1750106 (2017). https://doi.org/10.1142/S0219887817501067
Koufogiorgos, T., Markellos, M., Papantoniou, B.: The harmonicity of the Reeb vector field on contact metric 3-manifolds. Pac. J. Math. 234, 325–344 (2008)
Perrone, D.: Harmonic characteristic vector fields on contact metric three-manifolds. Bull. Austral. Math. Soc. 67(2), 305–315 (2003)
Welyczko, J.: Para-CR structures on almost paracontact metric manifolds. J. Appl. Anal. 20(2), 105–117 (2014)
Zamkovoy, S.: Canonical connections on paracontact manifolds. Ann. Glob. Anal. Geom. 36, 37–60 (2009)
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Küpeli Erken, I., Murathan, C. Ricci collineations on 3-dimensional paracontact metric manifolds . Afr. Mat. 29, 665–675 (2018). https://doi.org/10.1007/s13370-018-0568-2
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DOI: https://doi.org/10.1007/s13370-018-0568-2