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472
Copolarity of isometric actions
, 2008
"... We introduce a new integral invariant for isometric actions of compact Lie groups, the copolarity. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In particular, we develop some of the structural theory of copolari ..."
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Cited by 8 (3 self)
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We introduce a new integral invariant for isometric actions of compact Lie groups, the copolarity. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In particular, we develop some of the structural theory
PROPER ISOMETRIC ACTIONS
, 811
"... In this short note we use a theorem by Helgason to give an easy proof of two results on proper isometric actions (theorems 4 and 5). Throughout this paper we assume that M is a connected and complete Riemannian manifold. We denote by I(M) the full isometry group of M. It is a well known fact that I( ..."
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Cited by 1 (0 self)
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In this short note we use a theorem by Helgason to give an easy proof of two results on proper isometric actions (theorems 4 and 5). Throughout this paper we assume that M is a connected and complete Riemannian manifold. We denote by I(M) the full isometry group of M. It is a well known fact that I
A SURVEY ON THE GEOMETRY OF ISOMETRIC ACTIONS
"... We survey on our results on the geometry of the orbits of isometric actions of compact Lie groups on complete Riemannian manifolds. 1 ..."
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We survey on our results on the geometry of the orbits of isometric actions of compact Lie groups on complete Riemannian manifolds. 1
Notes on affine isometric actions of discrete groups
, 1997
"... 1. Affine isometric actions of semisimple groups of rank 1. 2. General remarks on affine isometric actions. 3. Rigidity for affine isometric actions. 4. Rtrees and related affine isometric actions ..."
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Cited by 2 (0 self)
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1. Affine isometric actions of semisimple groups of rank 1. 2. General remarks on affine isometric actions. 3. Rigidity for affine isometric actions. 4. Rtrees and related affine isometric actions
Isometric Actions And Harmonic Morphisms
 Math. Proc. Cambridge Philos. Soc
, 1999
"... We give the necessary and sufficient condition for a Riemannian foliation, of arbitrary dimension, locally generated by Killing fields to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained. Introduction It is wellknown that a Riemannian foliation ..."
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Cited by 4 (2 self)
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We give the necessary and sufficient condition for a Riemannian foliation, of arbitrary dimension, locally generated by Killing fields to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained. Introduction It is wellknown that a Riemannian foliation with minimal leaves has the property that it produces harmonic morphisms i.e. its leaves are locally fibres of submersive harmonic morphisms. This is an immediate consequence of the fact that Riemannian submersions with minimal fibres are harmonic morphisms. More generally, a Riemannian foliation (of codimension not equal to two) produces harmonic morphisms if and only if the vector field determined by the mean curvatures of the leaves is locally a gradient vector field. This is a consequence of the fundamental equation of P. Baird and J. Eells [1] (see Proposition 1.2 below). Although this condition is quite simple, there were not known many examples of such Riemannian foliations; our work...
Isometric actions of simple Lie groups
"... on pseudoRiemannian manifolds By Raul QuirogaBarranco* Let M be a connected compact pseudoRiemannian manifold acted upon topologically transitively and isometrically by a connected noncompact simple Lie group G. If m0, n0 are the dimensions of the maximal lightlike subspaces tangent to M and G, res ..."
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on pseudoRiemannian manifolds By Raul QuirogaBarranco* Let M be a connected compact pseudoRiemannian manifold acted upon topologically transitively and isometrically by a connected noncompact simple Lie group G. If m0, n0 are the dimensions of the maximal lightlike subspaces tangent to M and G
Isometric Actions Of Lie Groups And Invariants
, 1997
"... Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Polynomial Invariant Theory . . . . . . . . . . . . . . . . . . . . 5 3. C 1 Invariant Theory of Compact Lie Groups . . . . . . . . . . . . . 11 4. Transformation Groups . . . . . . . . . . . . . . . . . . . . . . . 34 5. ..."
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. Proper Actions . . . . . . . . . . . . . . . . . . . . . . . . . . 41 6. Riemannian Gmanifolds . . . . . . . . . . . . . . . . . . . . . . 48 7. Riemannian Submersions . . . . . . . . . . . . . . . . . . . . . . 57 8. Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 9
Results 1  10
of
472