Abstract: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.
Keywords: locally homogeneous spaces, curvature homogeneous spaces, totally geodesic foliations
AMS Subject Classification: 53C30, 53B20