- Arvanitoyeorgos, An introduction to Lie groups and the geometry of homogeneous spaces, vol. 22 of Student Mathematical Library, American Mathematical Society, Providence, RI, 2003. Translated from the 1999 Greek original and revised by the author.
- Bicˇak and J. Podolsk´ y´, Gravitational waves in vacuum spacetimes with cosmological constant. I. Classification and geometrical properties of nontwisting type N solutions, J. Math. Phys., 40 (1999), pp. 4495–4505.
- , Gravitational waves in vacuum spacetimes with cosmological constant. II. Deviation of geodesics and interpretation of nontwisting type N solutions, J. Math. Phys., 40 (1999), pp. 4506–4517.
- M. J. Calderbank and H. Pedersen, Einstein-Weyl geometry, in Surveys in differential geometry: essays on Einstein manifolds, vol. 6 of Surv. Differ. Geom., Int. Press, Boston, MA, 1999, pp. 387–423.
- Calvaruso, Siklos spacetimes as homogeneous Ricci solitons, Classical Quantum Gravity, 36 (2019), pp. 095011, 13.
- [6], Conformally flat Siklos metrics are Ricci solitons, Axioms, 9 (2020), pp. 1–13.
- , The Ricci soliton equation for homogeneous Siklos spacetimes, Note Mat., 41 (2021), pp. 31–44.
- Calvaruso and A. Fino, Ricci solitons and geometry of four-dimensional non-reductive homogeneous spaces, Canad. J. Math., 64 (2012), pp. 778–804.
- Calvaruso, M. Kaflou, and A. Zaeim, On the symmetries of Siklos spacetimes, Gen. Relativity Gravitation, 54 (2022), pp. Paper No. 60, 26.
- Calvaruso and A. Zaeim, The Bach-flat and conformally Einstein equations for Siklos spacetimes. Submitted.
- , A complete classification of Ricci and Yamabe solitons of non-reductive homogeneous 4-spaces, J. Geom. Phys., 80 (2014), pp. 15–25.
- -D. Cao, Recent progress on Ricci solitons, in Recent advances in geometric analysis, vol. 11 of Adv. Lect. Math. (ALM), Int. Press, Somerville, MA, 2010, pp. 1–38.
- T. Chru´sciel, H. S. Reall, and P. Tod, On non-existence of static vacuum black holes with degenerate components of the event horizon, Classical Quantum Gravity, 23 (2006), pp. 549–554.
- Defrise, Groupes d’isotropie et groupes de stabilit´e conforme dans les espaces Lorentziens, PhD thesis, Universit´e Libre de Bruxelles.
- Ehlers and W. Kundt, Exact solutions of the gravitational field equations, in Gravitation: An introduction to current research, Wiley, New York-London, 1962, pp. 49–101.
- Ghosh, Ricci soliton and Ricci almost soliton within the framework of Kenmotsu manifold, Carpathian Math. Publ., 11 (2019), pp. 56–69.
- Karami, A. Zaeim, and A. Haji-Badali, Ricci solitons and geometry of four dimensional Einstein-like neutral Lie groups, Period. Math. Hungar., 78 (2019), pp. 58–78.
- R. Ka˘ıgorodov, Einstein spaces of maximum mobility, Dokl. Akad. Nauk SSSR, 146, pp. 793–796.
- Lauret, Ricci soliton homogeneous nilmanifolds, Math. Ann., 319 (2001), pp. 715–733.
- , Ricci soliton solvmanifolds, J. Reine Angew. Math., 650 (2011), pp. 1–21.
- Mohseni, Vacuum polarization in Siklos spacetimes, Phys. Rev. D, 97 (2018), pp. 024006, 6.
- Nurowski and M. Randall, Generalized Ricci solitons, J. Geom. Anal., 26 (2016), pp. 1280–1345.
- Ozsvath, I. Robinson, and K. R´ ozga´ , Plane-fronted gravitational and electromagnetic waves in spaces with cosmological constant, J. Math. Phys., 26 (1985), pp. 1755–1761.
- Pahan, T. Dutta, and A. Bhattacharyya, Ricci soliton and η-Ricci soliton on generalized Sasakian space form, Filomat, 31 (2017), pp. 4051–4062.
- Podolsky´, Interpretation of the Siklos solutions as exact gravitational waves in the anti-de Sitter universe, Classical Quantum Gravity, 15 (1998), pp. 719–733.
- Podolsky´, Exact non-singular waves in the anti-de Sitter universe, Gen. Relativity Gravitation, 33 (2001), pp. 1093–1113.
- Podolsky and J. B. Griffiths´ , Impulsive waves in de sitter and anti-de sitter spacetimes generated by null particles with an arbitrary multipole structure, Class. Quantum Gravity, 15 (1998), p. 453.
- Randall, Local obstructions to projective surfaces admitting skew-symmetric Ricci tensor, J. Geom. Phys., 76 (2014), pp. 192–199.
- T. C. Siklos, Lobatchevski plane gravitational waves, in Galaxies, Axisymmetric Systems and Relativity, M. A. H. MacCallum, ed., Cambridge University Press, 1985.
- H.Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Exact solutions of Einstein’s field equations, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, second ed., 2003.
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