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Search: MSC category 53C50 ( Lorentz manifolds, manifolds with indefinite metrics )

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1. CJM 2011 (vol 64 pp. 778)

Calvaruso, Giovanni; Fino, Anna
Ricci Solitons and Geometry of Four-dimensional Non-reductive Homogeneous Spaces
We study the geometry of non-reductive $4$-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.

Keywords:non-reductive homogeneous spaces, pseudo-Riemannian metrics, Ricci solitons, Einstein-like metrics
Categories:53C21, 53C50, 53C25

2. CJM 2010 (vol 62 pp. 1037)

Calviño-Louzao, E.; García-Río, E.; Vázquez-Lorenzo, R.
Riemann Extensions of Torsion-Free Connections with Degenerate Ricci Tensor
{Correspondence} between torsion-free connections with {nilpotent skew-symmetric curvature operator} and IP Riemann extensions is shown. Some consequences are derived in the study of four-dimensional IP metrics and locally homogeneous affine surfaces.

Keywords:Walker metric, Riemann extension, curvature operator, projectively flat and recurrent affine connection
Categories:53B30, 53C50

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