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Ricci Solitons and Geometry of Four-dimensional Non-reductive Homogeneous Spaces
  Published:2011-12-23
 Printed: Aug 2012
Canadian Journal of Mathematics
  • Giovanni Calvaruso,
    Dipartimento di Matematica "E. De Giorgi", Università del Salento, Prov. Lecce-Arnesano, 73100 Lecce, Italy
  • Anna Fino,
    Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
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Abstract

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 non-reductive homogeneous spaces, pseudo-Riemannian metrics, Ricci solitons, Einstein-like metrics
MSC Classifications: 53C21, 53C50, 53C25 show english descriptions Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Lorentz manifolds, manifolds with indefinite metrics
Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C21 - Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
53C50 - Lorentz manifolds, manifolds with indefinite metrics
53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)
 
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