Related papers: Hyperbolic Structure of the Equilateral Pentagon

A group-theoretical approach to the construction of quasiperiodic tilings of a Euclidean plane, possessing five-fold symmetry, is applied. Of the infinitely many of variants of quasiperiodic partitions of the plane, possessing the dihedral…

This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…

We show that each connected component of the moduli space of smooth real binary quintics is isomorphic to an open subset of an arithmetic quotient of the real hyperbolic plane. Moreover, our main result says that the induced metric on this…

Negatively curved, or hyperbolic, regions of space in an FRW universe are a realistic possibility. These regions might occur in voids where there is no dark matter with only dark energy present. Hyperbolic space is strange and various…

We generalize the $(n+1)$-dimensional twisted $R$-Poisson topological sigma model with flux on a target Poisson manifold to a Lie algebroid. Analyzing consistency of constraints in the Hamiltonian formalism and the gauge symmetry in the…

Hyperbolic spaces have proven to be suitable for modeling data of hierarchical nature. As such we use the Poincare ball to embed sentences with the goal of proving how hyperbolic spaces can be used for solving Textual Entailment. To this…

We work with $N-$dimensional compact real hyperbolic space $X_{\Gamma}$ with universal covering $M$ and fundamental group $\Gamma$. Therefore, $M$ is the symmetric space $G/K$, where $G=SO_1(N,1)$ and $K=SO(N)$ is a maximal compact subgroup…

This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.

To every realizable oriented matroid there corresponds an arrangement of real hyperplanes. The homeomorphism type of the complexified complement of such an arrangement is completely determined by the oriented matroid. In this paper we study…

We characterize the image of the Poisson transform on any distinguished boundary of a Riemannian symmetric space of the noncompact type by a system of differential equations. The system corresponds to a generator system of a two sided…

We give a constructive proof that the Regge symmetry is a scissors congruence in hyperbolic space. The main tool is Leibon's construction for computing the volume of a general hyperbolic tetrahedron. The proof consists of identifying the…

In this paper we give a combinatorial description of the renormlization limits of infinitely renormalizable unimodal maps with {\it essentially bounded} combinatorics admitting quadratic-like complex extensions. As an application we…

We develop a notion of rank one properly convex domains (or Hilbert geometries) in the real projective space. This is in the spirit of rank one non-positively curved Riemannian manifolds and CAT(0) spaces. We define rank one isometries for…

We construct a quasiconformally homogeneous hyperbolic Riemann surface-other than the hyperbolic plane-that does not admit a bounded pants decomposition. Also, given a connected orientable topological surface of infinite type with compact…

In this paper we have build the modified Hamiltonian formalism for geometric objects like the Jacobi fields and metric tensors. In this approach Jacobi fields and metric tensors are mapped among manifold. As an application, we have mapped a…

Let F/Q be number field. The space of positive definite binary Hermitian forms over F form an open cone in a real vector space. There is a natural decomposition of this cone into subcones, which descend give rise to hyperbolic tessellations…

The conformal boundary of a hyperbolic $3$-manifold $M$ is a union of Riemann surfaces. If any of these Riemann surfaces has a nontrivial Teichm\"uller space, then the hyperbolic metric of $M$ can be deformed quasi-isometrically. These…

We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…

The celebrated Nash Embedding Theorem asserts that every closed Riemannian manifold can be isometrically embedded into a sufficiently high-dimensional Euclidean space. In this paper, we prove an analogous result in the conformally compact…

We classify edge-to-edge tilings of the sphere by congruent almost equilateral pentagons, in which four edges have the same length. Together with our earlier classifications of edge-to-edge tilings of the sphere by congruent equilateral…