On Lie Groups with Recurrent Curvature in Dimension Four

被引：0
作者：
Milad Bastami
Amirhesam Zaeim
Ali Haji-Badali
机构：
[1] University of Bonab,Department of Mathematics, Basic Sciences Faculty
[2] Payame Noor University,Department of Mathematics
来源：
Bulletin of the Iranian Mathematical Society | 2022年 / 48卷
关键词：
Curvature tensor; Lie group; Invariant metric; Recurrent curvature tensor; Ricci soliton; 53C50; 53C30; 53C25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we give a full classification of pseudo-Riemannian Lie groups of dimension four with non-trivial recurrent curvature tensor (i.e., non-locally symmetric). Then we investigate Ricci solitons on recurrent curvature Lie groups. Locally conformally flat examples of our classification have also been presented.
引用
收藏
页码：1037 / 1049
页数：12
相关论文
共 29 条
  • [1] Calvaruso G(2015)Four-dimensional pseudo-Riemannian homogeneous Ricci solitons Int. J. Geom. Methods Mod. Phys. 12 1550056-402
  • [2] Fino A(2013)Four-dimensional homogeneous Lorentzian manifolds Monatsh. Math. 174 377-509
  • [3] Calvaruso G(2013)Four-dimensional Lorentzian Lie groups Differ. Geom. Appl. 31 496-1044
  • [4] Zaeim A(2015)Neutral metrics on four-dimensional Lie groups J. Lie Theory 25 1023-361
  • [5] Calvaruso G(2013)Locally homogeneous four-dimensional manifolds of signature Math. Phys. Anal. Geom. 16 345-1513
  • [6] Zaeim A(1979)Generalized recurrent spaces Indian J. Pure Appl. Math. 10 1508-47
  • [7] Calvaruso G(2014)Homogeneity of Lorentzian three manifolds with recurrent curvature Math. Nachr. 287 32-967
  • [8] Zaeim A(2017)Ricci soliton on four-dimensional neutral Lie group J. Lie Theory 27 943-410
  • [9] Chaichi M(2020)Semi-symmetric four dimensional neutral Lie groups Czech Math. J. 70 393-78
  • [10] Zaeim A(2017)Ricci almost soliton on three-dimensional manifolds with recurrent curvature Mediterr. J. Math. 78 58-165
123