Ricci Solitons and Geometry of Four-dimensional Non-reductive Homogeneous Spaces

被引：37

作者：

Calvaruso, Giovanni ^{[1
]}

Fino, Anna ^{[2
]}

机构：

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

[2] Univ Turin, Dipartimento Matemat, I-10123 Turin, Italy

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2012年 / 64卷 / 04期

关键词：

non-reductive homogeneous spaces; pseudo-Riemannian metrics; Ricci solitons; Einstein-like metrics; LORENTZIAN MANIFOLDS; METRICS;

D O I：

10.4153/CJM-2011-091-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the geometry of non-reductive four-dimensional homogeneous spaces. In particular, after describing their Levi-Civita connection and curvature properties, we classify homogeneous Ricci solitons on these spaces, proving the existence of shrinking, expanding, and steady examples. For all the non-trivial examples we find, the Ricci operator is diagonalizable.

引用

页码：778 / 804

页数：27

共 26 条

[21] Towards physically motivated proofs of the Poincare and geometrization conjectures [J].