Geodesic
Geodesic graphs on special 7-dimensional g.o. manifolds
Archivum mathematicum, Tome 42 (2006) no. 5, pp. 213-227.

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In ( Dušek, Z., Kowalski, O. and Nikčević, S. Ž., New examples of Riemannian g.o. manifolds in dimension 7, Differential Geom. Appl. 21 (2004), 65–78.), the present authors and S. Nikčević constructed the 2-parameter family of invariant Riemannian metrics on the homogeneous manifolds $M=[{\rm SO}(5)\times {\rm SO}(2)]/{\rm U}(2)$ and $M=[{\rm SO}(4,1)\times {\rm SO}(2)]/{\rm U}(2)$. They proved that, for the open dense subset of this family, the corresponding Riemannian manifolds are g.o. manifolds which are not naturally reductive. Now we are going to investigate the remaining metrics (in the compact case).
Classification : 53C22, 53C30
Keywords: naturally reductive spaces; Riemannian g.o. spaces; geodesic graph 
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     title = {Geodesic graphs on special 7-dimensional g.o. manifolds},
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Dušek, Zdeněk; Kowalski, Oldřich. Geodesic graphs on special 7-dimensional g.o. manifolds. Archivum mathematicum, Tome 42 (2006) no. 5, pp. 213-227. http://geodesic.mathdoc.fr/item/ARM_2006__42_5_a8/