A note to a theorem by K. Sekigawa

Oldřich Kowalski

Displaying similar documents to “A note to a theorem by K. Sekigawa”

Curvature homogeneous riemannian manifolds

F. Tricerri, L. Vanhecke (1989)

Annales scientifiques de l'École Normale Supérieure

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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 $(M, g)$ satisfying the first odd Ledger condition is said to be of type $𝒜$ . 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...