Related papers: Hyperpolar actions on reducible symmetric spaces

We study the harmonic map equations for maps of a Riemann surface into a Riemannian symmetric space of compact type from the point of view of soliton theory. There is a well-known dressing action of a loop group on the space of harmonic…

We classify representations of compact connected Lie groups whose induced action on the unit sphere has an orbit space isometric to a Riemannian orbifold.

We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions--those for which the dimension of the…

We consider the action of a noncompact torus H on the compact quotient G/L, where G is a Lie group containing H and L is a uniform lattice in G. Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action…

In this paper, we classify Hamiltonian $S^1$-actions on compact, four dimensional symplectic orbifolds that have isolated singular points with cyclic orbifold structure groups, thus extending the classification due to Karshon to the…

We show that the inverse limit and the orbit map commute for actions of compact groups on compact Hausdorff spaces.

We develop a class of homeomorphisms on a compact homogeneous space of a transitive group action and show how the class sheds new light on a decomposition problem. We further use this class to show that every such homogeneous space in a…

This article deals with dihedral group actions on compact Riemann surfaces and the interplay between different geometric data associated to them. First, a bijective correspondence between geometric signatures and analytic representations is…

The aim of this paper is to classify the cohomogeneity one conformal actions on the 3-dimensional Einstein universe $Ein^{1;2}$ , up to orbit equivalence. In a recent paper [21], we studied the unique (up to conjugacy) irreducible action of…

Let M be a compact, connected and simply-connected Riemannian manifold, and suppose that G is a compact, connected Lie group acting on M by isometries. The dimension of the space of orbits is called the cohomogeneity of the action. If the…

We show that for a Hamiltonian action of a compact torus $G$ on a compact, connected symplectic manifold $M$, the $G$-equivariant cohomology is determined by the residual $S^1$ action on the submanifolds of $M$ fixed by codimension-1 tori.…

We consider a canonical $S^1$ action on $S^3$ which is defined by $(\rho,(z_1,z_2))\mapsto (z_1\rho^p,z_2\rho^q)$ for $\rho\in S^1$ and $(z_1,z_2)\in S^3\subset {\mathbb C}^2$. We consider a link consisting of finite orbits of this action,…

Let $\rho_0$ be an action of a Lie group on a manifold with boundary that is transitive on the interior. We study the set of actions that are topologically conjugate to $\rho_0$, up to smooth or analytic change of coordinates. We show that…

Among the ergodic actions of a compact quantum group $\mathbb{G}$ on possibly non-commutative spaces, those that are {\it embeddable} are the natural analogues of actions of a compact group on its homogeneous spaces. These can be realized…

We prove a criterion for an isometric action of a Lie group on a Riemannian manifold to be polar. From this criterion, it follows that an action with a fixed point is polar if and only if the slice representation at the fixed point is polar…

We consider partially hyperbolic abelian algebraic high-rank actions on compact homogeneous spaces obtained from simple indefinite orthogonal and unitary groups. In the first part of the paper, we show local differentiable rigidity for such…

We organize fundamental properties of quasi-Hamiltonian spaces on which a finite group acts, and we apply them to the theory of moduli spaces of flat connections on an oriented compact surface with boundary.

We show that a negative Einstein manifold admitting a proper isometric action of a connected unimodular Lie group with compact, possibly singular, orbit space splits isometrically as a product of a symmetric space and a compact negative…

The spatial Kepler problem with a perturbation satisfying the rotational symmetry w.r.t. the $z$-axis and the reflection symmetry w.r.t. the $(x, y)$-plane, can be reduced to an Hamiltonian system with 2 degrees of freedom after fixing the…

We introduce a Hopf algebroid associated to a proper Lie group action on a smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is equal to the de Rham cohomology of invariant differential forms. When the action is…