Complete classification of homogeneous structures on Lorentzian direct extensions of the Heisenberg group

[1] W. Ambrose and I. M. Singer, On homogeneous Riemannian manifolds, Duke Math. J., 25 (1958) 647–669.
[2] Y. Aryanejad, Some traits of homogeneous pseudo-Riemannian spaces with trivial isotropy, Mathematics and Society, 7 no. 1 (1401) 73–84. [In Persian]
[3] E. binz and S. Pods, The Geometry of Heisenberg Groups With Applications in Signal Theory, Optics, Quantization, and Field Quantization, American Mathematical Society, 2008.
[4] N. Bokan, T. Sukilovic and S. Vukmirovic, Lorentz geometry of 4-dimensional nilpotent Lie groups, Geom Dedicata, 177 (2015) 83–102.
[5] G. Calvaruso, Homogeneous structures on three-dimensional Lorentzian manifolds, J. Geom. Phys., 57 (2007) 1279–1291.
[6] G. Calvaruso and M. Castrillon-Lopez, Pseudo-Riemannian Homogeneous Structures, Developments in Math., Springer Nature, Switzerland, 2019.
[7] G. Calvaruso and M. Castrillon-Lopez, Cyclic Lorentzian Lie groups, Geom Dedicata, 181 (2016) 119–136.
[8] G. Calvaruso and A. Zaeim, Four-dimensional Lorentzian Lie groups, Differential Geometry and its Applications, 31 (2013) 496–509.
[9] P. M. Gadea and J. A. Oubina, Homogeneous pseudo-Riemannian structures and homogeneous almost para-Hermitian structures, Houston J. Math., 18 (1992) 449–465.
[10] P. M. Gadea, J. C. Gonzalez-Davila and J. A. Oubiña, Cyclic metric Lie groups, Monatsh. Math., 176 (2015) 219–239.
[11] P. M. Gadea, J. C. Gonzalez-Davila and J. A. Oubiña, Cyclic homogeneous Riemannian manifolds, Ann. Mat. Pura Appl., 195 (2016) 1619–1637.
[12] P. M. Gadea and J. A. Oubiña, Homogeneous Lorentzian structures on the Oscillator groups, Arch. Math., 73(1999) 311–320.
[13] P.M. Gadea and J. A. Oubiña, Homogeneous Riemannian structures on Berger 3-spheres, Proc. Edinb. Math. Soc., 48 no. 2 (2005) 375–387.
[14] L. Magnin, Sur les algebres de Lie nilpotents de dimension≤ 7, J. Geom. Phys., 3 no. 1 (1986) 119–144.
[15] J. Milnor, Curvature of left invariant metrics on Lie groups, Adv. Math., 21(1976) 293–329.
[16] B. O’Neill, Semi-Riemannian Geometry, New York: Academic Press, 1983.
[17] S. Rahmani, Maetriques de Lorentz sur les groupes de Lie unimodulaires de dimension trois, J. Geom. Phys., 9 (1992) 295–302.
[18] F. Tricerri and L. Vanhecke, Homogeneous Structures on Riemannian Manifolds, Cambridge University Press, Cambridge, 1983.
[19] A. Tohidfar and A. Zaeim, On Pseudo-Riemannian Cyclic Homogeneous Manifolds of Dimension Four, Journal of Lie Theory, 31 no. 1 (2021) 169–187.
[20] A. Zaeim, Y. Aryanejad, M. Gheitasi, On some conformally Einstein manifolds of dimension four, Mathematics and Society, 7 no. 2 (1401) 19–36. [In Persian]