On cohomogeneity one flat Riemannian manifolds

R. Mirzaie; S.M.B. Kashani

doi:10.1017/S0017089502020189

Abstract

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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.

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On cohomogeneity one flat Riemannian manifolds

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