Related papers: Toric moment mappings and Riemannian structures

A real toric space is a topological space which admits a well-behaved $\mathbb{Z}_2^k$-action. Real moment-angle complexes and real toric varieties are typical examples of real toric spaces. A real toric space is determined by a pair of a…

Let X be a compact oriented Riemannian manifold and let $\phi:X\to S^1$ be a circle-valued Morse function. Under some mild assumptions on $\phi$, we prove a formula relating: (a) the number of closed orbits of the gradient flow of $\phi$ of…

We list up all the possible local orbit types of hyperbolic or elliptic orbits for the isotropy representations of semisimple pseudo-Riemannian symmetric spaces. It is key to give a recipe to determine the local orbit types of hyperbolic…

Suppose that a compact $r$-dimensional torus $T^r$ acts in a holomorphic and Hamiltonian manner on polarized complex $d$-dimensional projective manifold $M$, with nowhere vanishing moment map $\Phi$. Assuming that $\Phi$ is transverse to…

The extensive analysis of the dynamics of relativistic spinning particles is presented. Using the coadjoint orbits method the Hamiltonian dynamics is explicitly described. The main technical tool is the factorization of general Lorentz…

In this paper, we consider generalized moment maps for Hamiltonian actions on $H$-twisted generalized complex manifolds introduced by Lin and Tolman \cite{Lin}. The main purpose of this paper is to show convexity and connectedness…

In this paper we study the coisotropic reduction in different types of dynamics according to the geometry of the corresponding phase space. The relevance of the coisotropic reduction is motivated by the fact that these dynamics can always…

In this paper, we develop results in the direction of an analogue of Sjamaar and Lerman's singular reduction of Hamiltonian symplectic manifolds in the context of reduction of Hamiltonian generalized complex manifolds (in the sense of Lin…

In this note, we introduce the concept of momentumly closed forms. A nondegenerate momentumly closed two-form defines a moment map that generalizes the classical notion associated with symplectic forms. We then develop an extended theory of…

We apply the coadjoint orbit technique to the group of area preserving diffeomorphisms (APD) of a 2D manifold, particularly to the APD of the semi-infinite cylinder which is identified with $w_{\infty}$. The geometrical action obtained is…

In this paper we generalize to coisotropic actions of compact Lie groups a theorem of Guillemin on deformations of Hamiltonian structures on compact symplectic manifolds. We show how one can reconstruct from the moment polytope the…

Consider a compact Lie group and a closed subgroup. Generalizing a result of Klyachko, we give a necessary and sufficient criterion for a coadjoint orbit of the subgroup to be contained in the projection of a given coadjoint orbit of the…

This paper introduces a quaternionic analogue of toric geometry by developing the theory of local $Q^n := Sp(1)^n$-actions on 4n-dimensional manifolds, modeled on the regular representation. We identify obstructions that measure the failure…

We compute the integral cohomology ring of configuration spaces of two points on a given real projective space. Apart from an integral class, the resulting ring is a quotient of the known integral cohomology of the dihedral group of order 8…

Consider a Hamiltonian torus action on a connected symplectic manifold M for which the associated moment map Phi is proper in some sense. Let Q be a closed submanifold of M. We show that under certain local conditions on Q one has…

The convexity theorem of Atiyah and Guillemin-Sternberg says that any connected compact manifold with Hamiltonian torus action has a moment map whose image is the convex hull of the image of the fixed point set. Sjamaar-Lerman proved that…

For seven-dimensional Riemannian manifolds equipped with a $G_2$-structure, we show in a full detailed way that all integral formulas and divergence equations, given by diverse authors, are agree with the ones displayed here in terms of the…

We develop a general structure theory for compact homogeneous Riemannian manifolds in relation to the co-index of symmetry. We will then use these results to classify irreducible, simply connected, compact homogeneous Riemannian manifolds…

There are several different notions of maximal torus actions on smooth manifolds, in various contexts: symplectic, Riemannian, complex. In the symplectic context, for the so-called isotropy-maximal actions, as well as for the weaker notion…

We define Wick-rotations by considering pseudo-Riemannian manifolds as real slices of a holomorphic Riemannian manifold. From a frame bundle viewpoint Wick-rotations between different pseudo-Riemannian spaces can then be studied through…