Geodesic
On cohomogeneity one flat Riemannian manifolds
Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 185-190

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We study the topological properties of cohomogeneity one flat manifolds and their orbits. Among other results we prove that principal orbits of R^n are isometric to R^{n-1} or S^k(c)\times R^{n-k-1}. We show that if M has one singular orbit, it is a totally geodesic submanifold of M and if M is orientable then there is at most one singular orbit. 
Mirzaie, R.; Kashani, S.M.B. On cohomogeneity one flat Riemannian manifolds. Glasgow mathematical journal, Tome 44 (2002) no. 2, pp. 185-190. doi: 10.1017/S0017089502020189
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     title = {On cohomogeneity one flat {Riemannian} manifolds},
     journal = {Glasgow mathematical journal},
     pages = {185--190},
     year = {2002},
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     doi = {10.1017/S0017089502020189},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089502020189/}
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