Tricerri, Franco; Vanhecke, Lieven Geodesic spheres and naturally reductive homogeneous spaces. (English) Zbl 0563.53040 Riv. Mat. Univ. Parma, IV. Ser. 10, 123-131 (1984). 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 Cited in 2 Documents MSC: 53C30 Differential geometry of homogeneous manifolds 53C20 Global Riemannian geometry, including pinching Keywords:geodesic spheres; reductive homogeneous spaces Citations:Zbl 0478.53035; Zbl 0134.178 PDFBibTeX XMLCite \textit{F. Tricerri} and \textit{L. Vanhecke}, Riv. Mat. Univ. Parma, IV. Ser. 10, 123--131 (1984; Zbl 0563.53040)