Displaying similar documents to “Three-dimensional curvature homogeneous hypersurfaces”

Curvature homogeneity of affine connections on two-dimensional manifolds

Oldřich Kowalski, Barbara Opozda, Zdeněk Vlášek (1999)

Colloquium Mathematicae

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Curvature homogeneity of (torsion-free) affine connections on manifolds is an adaptation of a concept introduced by I. M. Singer. We analyze completely the relationship between curvature homogeneity of higher order and local homogeneity on two-dimensional manifolds.

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.