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Curvature homogeneous spaces whose curvature tensors have large symmetries. (English) Zbl 1090.53050

The author studies curvature homogeneous spaces or locally homogeneous spaces whose curvatures are invariant by the action of “large” Lie subalgebras \(\mathfrak h\) of \({\mathfrak s}{\mathfrak o}(n)\). In the paper the author deals with the case of \({\mathfrak h} = {\mathfrak s}{\mathfrak o}(r)\oplus {\mathfrak s}{\mathfrak o}(n-r), (2\leq r\leq n-r)\), \({\mathfrak h}= {\mathfrak s}{\mathfrak o} (n-2)\), and the Lie algebras of Lie groups acting transitively on spheres, and classifies such curvature homogeneous spaces or locally homogeneous spaces.

MSC:

53C30 Differential geometry of homogeneous manifolds
53B20 Local Riemannian geometry
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