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Curvature homogeneous spaces whose curvature tensors have large symmetries

Kazumi Tsukada — 2002

Commentationes Mathematicae Universitatis Carolinae

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.

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