Three-dimensional semi-symmetric homogeneous Lorentzian manifolds
Three-dimensional semi-symmetric homogeneous Lorentzian manifolds
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三维半对称齐次洛伦兹流形
DOI：
10.1007/s10474-008-7194-7
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发表时间：
2008
影响因子：
0.9
通讯作者：
G. Calvaruso
中科院分区：
文献类型：
--
作者：
G. Calvaruso
由于Ricci算子的不同可能形式（塞格雷类型），洛伦兹流形曲率的半对称假设与黎曼情形有很大不同.事实上，一个半对称的齐次黎曼流形必然是对称的，而我们发现一些三维齐次洛伦兹流形是半对称的但不是对称的。给出了三维半对称齐次洛伦兹流形的完全分类。
Because of the different possible forms (Segre types) of the Ricci operator, semi-symmetry assumption for the curvature of a Lorentzian manifold turns out to have very different consequences with respect to the Riemannian case. In fact, a semi-symmetric homogeneous Riemannian manifold is necessarily symmetric, while we find some three-dimensional homogeneous Lorentzian manifolds which are semi-symmetric but not symmetric. The complete classification of three-dimensional semi-symmetric homogeneous Lorentzian manifolds is obtained.