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.
Ricci solitons and geometry of non-reductive homogeneous 4-spaces
FINO, Anna Maria
2012-01-01
Abstract
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.
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