Title:
|
Semi-symmetric four dimensional neutral Lie groups (English) |
Author:
|
Haji-Badali, Ali |
Author:
|
Zaeim, Amirhesam |
Language:
|
English |
Journal:
|
Czechoslovak Mathematical Journal |
ISSN:
|
0011-4642 (print) |
ISSN:
|
1572-9141 (online) |
Volume:
|
70 |
Issue:
|
2 |
Year:
|
2020 |
Pages:
|
393-410 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
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. (English) |
Keyword:
|
semi-symmetric |
Keyword:
|
Lie group, Ricci soliton |
MSC:
|
53C25 |
MSC:
|
53C30 |
MSC:
|
53C50 |
idZBL:
|
07217142 |
idMR:
|
MR4111850 |
DOI:
|
10.21136/CMJ.2019.0342-18 |
. |
Date available:
|
2020-06-17T12:32:51Z |
Last updated:
|
2022-07-04 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148236 |
. |
Reference:
|
[1] Arias-Marco, T., Kowalski, O.: Classification of 4-dimensional homogeneous D'Atri spaces.Czech. Math. J. 133 (2008), 203-239. Zbl 1174.53024, MR 2402535, 10.1007/s10587-008-0014-y |
Reference:
|
[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. Zbl 0482.53036, MR 0769130 |
Reference:
|
[3] Boeckx, E.: Einstein-like semi-symmetric spaces.Arch. Math., Brno 29 (1993), 235-240. Zbl 0807.53041, MR 1263125 |
Reference:
|
[4] Boeckx, E., Calvaruso, G.: When is the unit tangent sphere bundle semi-symmetric?.Tohoku Math. J., II. Ser. 56 (2004), 357-366. Zbl 1076.53032, MR 2075771, 10.2748/tmj/1113246672 |
Reference:
|
[5] Boeckx, E., Kowalski, O., Vanhecke, L.: Riemannian Manifolds of Conullity Two.World Scientific, Singapore (1996). Zbl 0904.53006, MR 1462887, 10.1142/9789812819970 |
Reference:
|
[6] Calvaruso, G.: Three-dimensional semi-symmetric homogeneous Lorentzian manifolds.Acta Math. Hung. 121 (2008), 157-170. Zbl 1199.53135, MR 2463255, 10.1007/s10474-008-7194-7 |
Reference:
|
[7] Calvaruso, G.: Semi-symmetric Lorentzian metrics and three-dimensional curvature homogeneity of order one.Abh. Math. Semin. Univ. Hamb. 79 (2009), 1-10. Zbl 1175.53077, MR 2541339, 10.1007/s12188-009-0018-z |
Reference:
|
[8] Calvaruso, G., Leo, B. De: Semi-symmetric Lorentzian three-manifolds admitting a parallel degenerate line field.Mediterr. J. Math. 7 (2010), 89-100. Zbl 1193.53146, MR 2645904, 10.1007/s00009-010-0029-0 |
Reference:
|
[9] Calvaruso, G., Fino, A.: Ricci solitons and geometry of four-dimensional non-reductive homogeneous spaces.Can. J. Math. 64 (2012), 778-804. Zbl 1252.53056, MR 2957230, 10.4153/CJM-2011-091-1 |
Reference:
|
[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. Zbl 1405.53054, MR 3349925, 10.1142/S0219887815500565 |
Reference:
|
[11] Calvaruso, G., Vanhecke, L.: Special ball-homogeneous spaces.Z. Anal. Anwend. 16 (1997), 789-800. Zbl 0892.53023, MR 1615680, 10.4171/ZAA/792 |
Reference:
|
[12] Calvaruso, G., Zaeim, A.: Neutral metrics on four-dimensional Lie groups.J. Lie Theory 25 (2015), 1023-1044. Zbl 1343.53071, MR 3345046 |
Reference:
|
[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. Zbl 1201.53046, MR 2648937 |
Reference:
|
[14] Haji-Badali, A., Karami, R.: Ricci solitons on four-dimensional neutral Lie groups.J. Lie Theory 27 (2017), 943-967. Zbl 06843179, MR 3622327 |
Reference:
|
[15] Jensen, G. R.: Homogeneous Einstein spaces of dimension four.J. Differ. Geom. 3 (1969), 309-349. Zbl 0194.53203, MR 0261487, 10.4310/jdg/1214429056 |
Reference:
|
[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. Zbl 07058278, MR 3919748, 10.1007/s10998-018-0262-z. |
Reference:
|
[17] O'Neill, B.: Semi-Riemannian Geometry: With Applications to Relativity.Pure and Applied Mathematics 103, Academic Press, New York (1983). Zbl 0531.53051, MR 0719023 |
Reference:
|
[18] Rahmani, S.: Métriques de Lorentz sur les groupes de Lie unimodulaires de dimension trois.J. Geom. Phys. 9 (1992), 295-302 French. Zbl 0752.53036, MR 1171140, 10.1016/0393-0440(92)90033-W |
Reference:
|
[19] Sekigawa, K.: On some 3-dimensional curvature homogeneous spaces.Tensor, New Ser. 31 (1977), 87-97. Zbl 0356.53016, MR 0464115 |
Reference:
|
[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. Zbl 0508.53025, MR 0683165, 10.4310/jdg/1214437486 |
Reference:
|
[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. Zbl 0237.53041, MR 0319109, 10.2748/tmj/1178241595 |
Reference:
|
[22] Zaeim, A., Karami, R.: Geometric consequences of four dimensional neutral Lie groups.Bull. Braz. Math. Soc. (N.S.) 50 (2019), 167-186. Zbl 07068771, MR 3935062, 10.1007/s00574-018-0097-5 |
. |