Related papers: Deforming ideal solid tori

Let M be a complete finite-volume hyperbolic 3-manifold with compact non-empty geodesic boundary and k toric cusps, and let T be a geometric partially truncated triangulation of M. We show that the variety of solutions of consistency…

We study the dimensional aspect of the geometry of quantum spaces. Introducing a physically motivated notion of the scaling dimension, we study in detail the model based on a fuzzy torus. We show that for a natural choice of a deformed…

Cubic forms in three variables are parametrised by points of $\P^9$. We study the subvarieties in this space defined by decomposable forms. Specifically, we calculate the equivariant minimal resolutions of these varieties and describe their…

We describe the first-order variations of the angles of Euclidean, spherical or hyperbolic polygons under infinitesimal deformations such that the lengths of the edges do not change. Using this description, we introduce a vector-valued…

We consider isomonodromic deformations of connections with a simple pole on the torus, motivated by the elliptic version of the sixth Painlev\'e equation. We establish an extended symmetry, complementing known results. The Calogero-Moser…

We consider synchrony patterns in coupled phase oscillator networks that correspond to invariant tori. For specific nongeneric coupling, these tori are equilibria relative to a continuous symmetry action. We analyze how the invariant tori…

There are many interesting dynamical systems in which degenerate invariant tori appear. We give conditions under which these degenerate tori have stable and unstable invariant manifolds, with stable and unstable directions having arbitrary…

We consider a compact hyperbolic tetrahedron of a general type. It is a convex hull of four points called vertices in the hyperbolic space $\mathbb{H}^3$. It can be determined by the set of six edge lengths up to isometry. For further…

We show that a weight variety, which is a quotient of a flag variety by the maximal torus, admits a flat degeneration to a toric variety. In particular, we show that the moduli spaces of spatial polygons degenerate to polarized toric…

In a companion paper [Pitrou, Phys. Rev. E 97, 043115 (2018)], a formalism allowing to describe viscous fibers as one-dimensional objects was developed. We apply it to the special case of a viscous fluid torus. This allows to highlight the…

Perfect fluid tori with uniform distribution of the specific angular momentum orbiting the Kerr-de Sitter black holes or naked singularities are studied. Closed equipotential surfaces corresponding to stationary toroidal discs are allowed…

It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: We consider integrable deformations of a non-flat Liouville metric in a…

We provide a construction of examples of semistable degeneration via toric geometry. The applications include a higher dimensional generalization of classical degeneration of K3 surface into 4 rational components, an algebraic geometric…

An exact solution of the vacuum Einstein equations with a cosmological constant is exhibited which can perhaps be used to describe the interior of compact rotating objects. The physical part of this solution has the topology of a torus,…

Torus orbifolds are topological generalization of symplectic toric orbifolds. We give a construction of smooth orbifolds with torus actions whose boundary is a disjoint union of torus orbifolds using toric topological method. As a result,…

The reduced system in the problem of the inertial motion of a rigid body with a fixed point (the Euler case) is equivalent, by the Maupertuis principle, to some geodesic flow on the 2-sphere. We describe the phase topology of this case…

L. Paoluzzi constructed a family of compact orientable three-dimensional hyperbolic manifolds with totally geodesic boundary, which were, by construction, closely related to the three-dimensional torus. This paper gives their complete…

There exists a smooth foliation with 3 singular points on the two-dimensional torus such that any lifting of a leaf of this foliation on the universal covering of the torus is a dense subset of the covering.

We describe the family of real structures $\sigma$ on principal holomorphic torus bundles $X$ over tori, and prove its connectedness when the complex dimension is at most three. From this and previous results of the authors follows that the…

Asymptotically flat, time-symmetric, axially symmetric and conformally flat initial data for vacuum general relativity are studied numerically on $R^3$ with the interior of a standard torus cut out. By the choice of boundary condition the…