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Geodesic spheres and naturally reductive homogeneous spaces. (English) Zbl 0563.53040

W. Ziller [Math. Ann. 259, 351-358 (1982; Zbl 0478.53035)] proved that all geodesic spheres in two-point homogeneous spaces, except for the Cayley plane, are naturally reductive homogeneous spaces. The present authors give a new proof of this result by using a technique of W. Ambrose and I. M. Singer [Duke Math. J. 25, 647-669 (1958; Zbl 0134.178)].
Reviewer: O.Kowalski

MSC:

53C30 Differential geometry of homogeneous manifolds
53C20 Global Riemannian geometry, including pinching
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