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Annals of Global Analysis and Geometry

, Volume 11, Issue 3, pp 197–211 | Cite as

RiemannianG-manifold with one-dimensional orbit space

  • Andrey V. Alekseevsky
  • Dmitry V. Alekseevsky
Article
  • 242 Downloads

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.

Key words

Riemannian G-manifold action of compact Lie group orbit space Weyl group normal geodesic sections cohomogeneous one manifold 

MSC 1991

53C35 53C30 53C21 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Andrey V. Alekseevsky
    • 1
  • Dmitry V. Alekseevsky
    • 2
  1. 1.Belozuorsky LaboratoryMoscow UniversityMoscowRussia
  2. 2.Center „Sophus Lie“MoscowRussia

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