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Keywords:
locally homogeneous spaces; curvature homogeneous spaces; totally geodesic foliations
locally homogeneous spaces; curvature homogeneous spaces; totally geodesic foliations
Summary:
We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of ``large" Lie subalgebras $\frak{h}$ of $\frak{so}(n)$. In this paper we deal with the cases of $\frak{h}=\frak{so}(r) \oplus \frak{so}(n-r)$ $(2\leq r \leq n-r)$, $\frak{so}(n-2)$, 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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