• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.151-163
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• 2006

Any simply connected fixed point cohomogeneity one riemannian manifold with positive sectional curvature is diffeomorphic to one of the compact rank one symmetric spaces.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.587-599
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• 2000

In this paper we study some nonpositively curved Riemannian manifolds acted on by a Lie group of isometries with principal orbits of codimension one. Among other results it is proved that if the universal covering manifold satisfies some conditions then every nonexceptional singular orbit is a totally geodesic submanifold. When M is flat and is not toruslike, it is proved that either each orbit is isometric to $R^k\timesT^m$or there is a singular orbit. If the singular orbit is unique and nonexceptional, then it is isometric to $R^k\timesT^m$.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.799-807
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• 2007

In this paper we study non-simply connected Riemannian manifolds of constant positive curvature which have an orbit of codimension one under the action of a connected closed Lie subgroup of isometries. When the action is reducible we characterize the orbits explicitly. We also prove that in some cases the manifold is homogeneous.