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Displaying similar documents to “Curvature tensors and Singer invariants of four-dimensional homogeneous spaces”

Curvature homogeneous spaces whose curvature tensors have large symmetries

Kazumi Tsukada (2002)

Commentationes Mathematicae Universitatis Carolinae

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We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of “large" Lie subalgebras 𝔥 of 𝔰𝔬 ( n ) . In this paper we deal with the cases of 𝔥 = 𝔰𝔬 ( r ) ⊕ 𝔰𝔬 ( n - r ) ( 2 ≤ r ≤ n - r ) , 𝔰𝔬 ( n - 2 ) , and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.

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.