相关论文: Triangular hyperbolic buildings

We discuss geometric properties of covers of closed hyperbolic manifolds of dimension $n\geq 3$, branched along a totally geodesic codimension two submanifold $\Sigma$. The results are mostly known to the experts but hard to find in the…

We consider a volume maximization program to construct hyperbolic structures on triangulated 3-manifolds, for which previous progress has lead to consider angle assignments which do not correspond to a hyperbolic metric on each simplex. We…

The notions of holomorphic symplectic structures and hypercomplex structures on Courant algebroids are introduced and then proved to be equivalent. These generalize hypercomplex triples and holomorphic symplectic 2-forms on manifolds…

A symplectic form is called hyperbolic if its pull-back to the universal cover is a differential of a bounded one-form. The present paper is concerned with the properties and constructions of manifolds admitting hyperbolic symplectic forms.…

We realize 4 of the 6 closed orientable flat 3-manifolds as a cusp section of an orientable finite-volume hyperbolic 4-manifold whose symmetry group acts transitively on the set of cusps.

The hexabasic book is the cone of the 1-dimensional skeleton of the union of two tetrahedra glued along a common face. The universal 3-dimensional polyhedron UP is the product of a segment and the hexabasic book. We show that any…

By using unramified cohomology groups, we construct a full sequence of cohomological invariants for hermitian forms of any type (orthogonal, symplectic or unitary) that can be used to detect hyperbolicity. The base central simple algebras…

Since there is no hyperbolic Dehn filling theorem for higher dimensions, it is challenging to construct explicit hyperbolic manifolds of small volume in dimension at least four. Here, we build up closed hyperbolic 4-manifolds of volume…

In this paper we will consider the 2-fold symmetric complex hyperbolic triangle groups generated by three complex reflections through angle 2pi/p with p no smaller than 2. We will mainly concentrate on the groups where some elements are…

We calculate the Jacobian matrix of the dihedral angles of a generalized hyperbolic tetrahedron as functions of edge lengths and find the complete set of symmetries of this matrix.

We study certain group actions on triangle buildings and their boundaries and some von Neumann algebras which can be constructed from them. In particular, for buildings of order $q\geq 3$ certain natural actions on the boundary are…

Using the method of C. V\"or\"os, we establish results on hyperbolic plane geometry, related to triangles. In this note we investigate the orthocenter, the concept of isogonal conjugate and some further center as of the symmedian of a…

We prove that every complete finite-volume hyperbolic 3-manifold $M$ that is tessellated into (embedded) right-angled regular polyhedra (dodecahedra or ideal octahedra) embeds geodesically in a complete finite-volume connected orientable…

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…

Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…

We prove that every closed oriented 3-manifold admits a hyperbolic cone-manifold structure with cone-angle arbitrarily close to 2pi.

We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.

We give a short proof of the contractibility of the space of geodesic triangulations with fixed combinatorial type of a convex polygon in the Euclidean plane. Moreover, for any $n>0$, we show that there exists a space of geodesic…

We show that the standard method for constructing closed hyperbolic manifolds of arbitrary dimension possessing reflective symmetries typically produces reflections whose fixed point sets are nonseparating.

We construct first examples of discrete geometrically finite subgroups of PU(2,1) which contain parabolic elements, and are isomorphic to surface groups.