Algebraic restrictions on geometric realizations of curvature models

Corey Dunn; Zoë Smith

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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 $𝔥 = 𝔰𝔬 (r) \oplus 𝔰𝔬 (n - r)$ $(2 \leq r \leq n - r)$ , $𝔰𝔬 (n - 2)$ , and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.