Curvature homogeneous riemannian manifolds
F. Tricerri, L. Vanhecke (1989)
Annales scientifiques de l'École Normale Supérieure
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Displaying similar documents to “A note to a theorem by K. Sekigawa”
Curvature homogeneous riemannian manifolds
Four-dimensional curvature homogeneous spaces
Kouei Sekigawa, Hiroshi Suga, Lieven Vanhecke (1992)
Commentationes Mathematicae Universitatis Carolinae
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We prove that a four-dimensional, connected, simply connected and complete Riemannian manifold which is curvature homogeneous up to order two is a homogeneous Riemannian space.
Classification of 4-dimensional homogeneous D'Atri spaces
Teresa Arias-Marco, Oldřich Kowalski (2008)
Czechoslovak Mathematical Journal
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The property of being a D’Atri space (i.e., a space with volume-preserving symmetries) is equivalent to the infinite number of curvature identities called the odd Ledger conditions. In particular, a Riemannian manifold satisfying the first odd Ledger condition is said to be of type . The classification of all 3-dimensional D’Atri spaces is well-known. All of them are locally naturally reductive. The first attempts to classify all 4-dimensional homogeneous D’Atri spaces were done in...