Related papers: Orbit Spaces of Linear Circle Actions

In the present paper, we prove that no infinite group acts isometrically, effectively, and properly discontinuously on a certain class of Lorentzian manifolds that are not necessarily homogeneous.

We prove some algebraic results on the ring of matrix differential operators over a differential field in the generality of non-commutative principal ideal rings. These results are used in the theory of non-local Poisson structures.

We study isometric cohomogeneity one actions on the (n+1)-dimensional Minkowski space up to orbit-equivalence. We give examples of isometric cohomogeneity one actions on the Minkowski space whose orbit spaces are non-Hausdorff. We show that…

We propose a nonlinear orbital magnetoelectric effect, which generates orbital magnetization quadratically in centrosymmetric materials where the linear orbital magnetoelectric effect is strictly forbidden. Using extended semiclassical…

In this paper we introduce the notion of orbit equivalence for semigroup actions and the concept of generalized linear control system on smooth manifold. The main goal is to prove that, under certain conditions, the semigroup system of a…

For actions with a dense orbit of a connected noncompact simple Lie group $G$, we obtain some global rigidity results when the actions preserve certain geometric structures. In particular, we prove that for a $G$-action to be equivalent to…

Several examples of pairs of isospectral planar domains have been produced in the two-dimensional Euclidean space by various methods. We show that all these examples rely on the symmetry between points and blocks in finite projective…

We construct smooth actions of arbitrary compact Lie groups on complex projective spaces, such that the corresponding transformations arising from the group action do not preserve any symplectic structure on the complex projective space.

In this paper we explicitly evaluate the one-loop effective action in four dimensions for scalar and spinor fields under the influence of a strong, covariantly constant, magnetic field in curved spacetime. In the framework of zeta function…

We develop algorithms and computer programs which verify criteria of properness of discrete group actions on semisimple homogeneous spaces. We apply these algorithms to find new examples of non-virtually abelian discontinuous group actions…

The orbit-fixing deformation spaces of $C^\infty$ locally free actions of simply connected Lie groups on closed $C^\infty$ manifolds have been studied by several authors. In this paper we reformulate the deformation space by imitating the…

We show that formal isomorphism of intransitive linear Lie equations along transversal to the orbits can be extended to neighborhoods of these transversal. In analytic cases, the word formal is dropped from theorems. Also, we associate an…

We study in this article the mathematical properties of a class of orbital-free kinetic energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic energy…

Optical activity, the power of a medium to rotate the polarization of a light beam, has contributed significantly to molecular structure assessments in stereochemistry, biomolecular science and crystallography. Thus far, it is commonly…

The strata of the moduli spaces of Abelian differentials are non-homogenous spaces carrying natural bi-algebraic structures. Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties…

This paper presents a survey of recent and not so recent results concerning the study of smooth homeomorphisms of the circle with a finite number of non-flat critical points, an important topic in the area of One-dimensional Dynamics. We…

We demonstrate experimentally and numerically that nonplanar chiral metamaterials give giant optical activity, circular dichroism, and negative refractive index. The transmission, reflection, and the retrieval results of the experiments…

This paper studies geometric structures on noncommutative hypersurfaces within a module-theoretic approach to noncommutative Riemannian (spin) geometry. A construction to induce differential, Riemannian and spinorial structures from a…

In this paper we first describe the geometry of the Newton polyhedra of polynomials invariant under certain linear Hamiltonian circle actions. From the geometry of the polyhedra, various Poisson structures on the orbit spaces of the actions…

In this paper we relate the study of actions of discrete groups over connected manifolds to that of their orbit spaces seen as differentiable stacks. We show that the orbit stack of a discrete dynamical system on a simply connected manifold…