Abstract
Cohomogeneity one RiemannianG-manifolds (i.e. Riemannian manifolds with a groupG of isometries having an orbit of codimension one) are studied. A description of such manifolds (up to some normal equivalence) is given in terms of Lie subgroups of Lie groupG. The twist of a geodesic normal to all orbits is defined as the number of intersections with a singular orbit. It is equal to the order of some Weyl group, associated with theG-manifold. Some results about possible values of the twist are obtained.
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Alekseevsky, A.V., Alekseevsky, D.V. RiemannianG-manifold with one-dimensional orbit space. Ann Glob Anal Geom 11, 197–211 (1993). https://doi.org/10.1007/BF00773366
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DOI: https://doi.org/10.1007/BF00773366
Key words
- Riemannian G-manifold
- action of compact Lie group
- orbit space
- Weyl group
- normal geodesic
- sections
- cohomogeneous one manifold