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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 of . In this paper we deal with the cases of
, , and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.
We show that the Singer invariant of a four-dimensional homogeneous space is at most .
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