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Cohomogeneity one actions on symmetric spaces of noncompact type
-
Jürgen Berndt
and
Hiroshi Tamaru
Published/Copyright:
March 13, 2012
Abstract.
An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type in terms of orbit equivalence. As a consequence, we find many new examples of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type. We apply our conceptual approach to derive explicit classifications of cohomogeneity one actions on some symmetric spaces.
Received: 2011-03-23
Revised: 2011-12-07
Published Online: 2012-03-13
Published in Print: 2013-10-01
© 2013 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Unified approach to the classification of actions of discrete amenable groups on injective factors
- Isoperimetric control of the spectrum of a compact hypersurface
- Weighted divisor sums and Bessel function series. III
- Quasilinear parabolic equations and the Ricci flow on manifolds with boundary
- On the noncommutative Bondal–Orlov conjecture
- Cohomogeneity one actions on symmetric spaces of noncompact type
- Isoparametric functions and exotic spheres
- The rationality of the moduli spaces of trigonal curves of odd genus
- On Nichols algebras of diagonal type
