Semi-symmetric four dimensional neutral Lie groups
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 393-410 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The present paper is concerned with obtaining a classification regarding to four-dimensional semi-symmetric neutral Lie groups. Moreover, we discuss some geometric properties of these spaces. We exhibit a rich class of non-Einstein Ricci soliton examples.
The present paper is concerned with obtaining a classification regarding to four-dimensional semi-symmetric neutral Lie groups. Moreover, we discuss some geometric properties of these spaces. We exhibit a rich class of non-Einstein Ricci soliton examples.
DOI : 10.21136/CMJ.2019.0342-18
Classification : 53C25, 53C30, 53C50
Keywords: semi-symmetric; Lie group, Ricci soliton
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Haji-Badali, Ali; Zaeim, Amirhesam. Semi-symmetric four dimensional neutral Lie groups. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 2, pp. 393-410. doi: 10.21136/CMJ.2019.0342-18

[1] Arias-Marco, T., Kowalski, O.: Classification of 4-dimensional homogeneous D'Atri spaces. Czech. Math. J. 133 (2008), 203-239. | DOI | MR | JFM

[2] Bérard-Bérgery, L.: Les espaces homogènes Riemanniens de dimension 4. Géométrie Riemannienne en Dimension 4. Séminaire Arthur Besse Cedic, Paris (1981), 40-60 French. | MR | JFM

[3] Boeckx, E.: Einstein-like semi-symmetric spaces. Arch. Math., Brno 29 (1993), 235-240. | MR | JFM

[4] Boeckx, E., Calvaruso, G.: When is the unit tangent sphere bundle semi-symmetric?. Tohoku Math. J., II. Ser. 56 (2004), 357-366. | DOI | MR | JFM

[5] Boeckx, E., Kowalski, O., Vanhecke, L.: Riemannian Manifolds of Conullity Two. World Scientific, Singapore (1996). | DOI | MR | JFM

[6] Calvaruso, G.: Three-dimensional semi-symmetric homogeneous Lorentzian manifolds. Acta Math. Hung. 121 (2008), 157-170. | DOI | MR | JFM

[7] Calvaruso, G.: Semi-symmetric Lorentzian metrics and three-dimensional curvature homogeneity of order one. Abh. Math. Semin. Univ. Hamb. 79 (2009), 1-10. | DOI | MR | JFM

[8] Calvaruso, G., Leo, B. De: Semi-symmetric Lorentzian three-manifolds admitting a parallel degenerate line field. Mediterr. J. Math. 7 (2010), 89-100. | DOI | MR | JFM

[9] Calvaruso, G., Fino, A.: Ricci solitons and geometry of four-dimensional non-reductive homogeneous spaces. Can. J. Math. 64 (2012), 778-804. | DOI | MR | JFM

[10] Calvaruso, G., Fino, A.: Four-dimensional pseudo-Riemannian homogeneous Ricci solitons. Int. J. Geom. Methods Mod. Phys. 12 (2015), Article ID 1550056, 21 pages. | DOI | MR | JFM

[11] Calvaruso, G., Vanhecke, L.: Special ball-homogeneous spaces. Z. Anal. Anwend. 16 (1997), 789-800. | DOI | MR | JFM

[12] Calvaruso, G., Zaeim, A.: Neutral metrics on four-dimensional Lie groups. J. Lie Theory 25 (2015), 1023-1044. | MR | JFM

[13] Cao, H.-D.: Recent progress on Ricci solitons. Recent advances in geometric analysis Y.-I. Lee et al. Advanced Lectures in Mathematics (ALM) 11, International Press, Somerville (2010), 1-38. | MR | JFM

[14] Haji-Badali, A., Karami, R.: Ricci solitons on four-dimensional neutral Lie groups. J. Lie Theory 27 (2017), 943-967. | MR | JFM

[15] Jensen, G. R.: Homogeneous Einstein spaces of dimension four. J. Differ. Geom. 3 (1969), 309-349. | DOI | MR | JFM

[16] Karami, R., Zaeim, A., Haji-Badali, A.: Ricci solitons and geometry of four dimensional Einstein-like neutral Lie groups. Period. Math. Hung. 78 (2019), 58-78. | DOI | MR | JFM

[17] O'Neill, B.: Semi-Riemannian Geometry: With Applications to Relativity. Pure and Applied Mathematics 103, Academic Press, New York (1983). | MR | JFM

[18] Rahmani, S.: Métriques de Lorentz sur les groupes de Lie unimodulaires de dimension trois. J. Geom. Phys. 9 (1992), 295-302 French. | DOI | MR | JFM

[19] Sekigawa, K.: On some 3-dimensional curvature homogeneous spaces. Tensor, New Ser. 31 (1977), 87-97. | MR | JFM

[20] Szabo, Z. I.: Structure theorems on Riemannian spaces satsfying $R(X,Y)\cdot R=0$ I: The local version. J. Differ. Geom. 17 (1982), 531-582. | DOI | MR | JFM

[21] Takagi, H.: An example of Riemannian manifold satisfying $R(X,Y)\cdot R$ but not $\nabla R = 0$. Tohoku Math. J. 24 (1972), 105-108. | DOI | MR | JFM

[22] Zaeim, A., Karami, R.: Geometric consequences of four dimensional neutral Lie groups. Bull. Braz. Math. Soc. (N.S.) 50 (2019), 167-186. | DOI | MR | JFM

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