Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds

被引：60

作者：

Calvaruso, G. ^{[1
]}

机构：

[1] Univ Lecce, Dipartimento Matemat E De Giorgi, I-73100 Lecce, Italy

来源：

GEOMETRIAE DEDICATA | 2007年 / 127卷 / 01期

关键词：

Lorentzian homogeneous spaces; Einstein-like metrics; symmetric spaces; naturally reductive spaces;

D O I：

10.1007/s10711-007-9163-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We completely classify three-dimensional homogeneous Lorentzian manifolds, equipped with Einstein-like metrics. Similarly to the Riemannian case (E. Abbena et al., Simon Stevin Quart J Pure Appl Math 66:173-182, 1992), if (M, g) is a three-dimensional homogeneous Lorentzian manifold, the Ricci tensor of (M, g) being cyclic-parallel (respectively, a Codazzi tensor) is related to natural reductivity (respectively, symmetry) of (M, g). However, some exceptional examples arise.

引用

页码：99 / 119

页数：21

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