Problems in Hyperbolic Geometry
نویسنده
چکیده
The purpose of this document is to list some outstanding questions in the subject of hyperbolic geometry (real, complex, quaternionic, and the Cayley plane), with the primary focus on the latter three. This list was inspired by the problem sessions held at the conference on Complex Hyperbolic Geometry in Luminy (CIRM) in July of 2003. The questions are roughly grouped by similarity. The name(s) next to the questions are the individual(s) who submitted the question. In the absence of a name, the problem was submitted anonymously.
منابع مشابه
Metric and periodic lines in the Poincare ball model of hyperbolic geometry
In this paper, we prove that every metric line in the Poincare ball model of hyperbolic geometry is exactly a classical line of itself. We also proved nonexistence of periodic lines in the Poincare ball model of hyperbolic geometry.
متن کاملAn Extension of Poincare Model of Hyperbolic Geometry with Gyrovector Space Approach
The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. In [1], Ungar and Chen showed that the algebra of the group $SL(2,mathbb C)$ naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the Lorentz group and its underlying hyperbolic geometry. They defined the Chen addition and then Chen model of hyperbolic geomet...
متن کاملSpatial Analysis in curved spaces with Non-Euclidean Geometry
The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...
متن کاملSOLVING LINEAR SIXTH-ORDER BOUNDARY VALUE PROBLEMS BY USING HYPERBOLIC UNIFORM SPLINE METHOD
In this paper, a numerical method is developed for solving a linear sixth order boundaryvalue problem (6VBP ) by using the hyperbolic uniform spline of order 3 (lower order). Thereis proved to be first-order convergent. Numerical results confirm the order of convergencepredicted by the analysis.
متن کاملStatement : Jessica
A 3–manifold is often described combinatorially, for example by a knot diagram, or by gluing a collection of polyhedra, or by attaching handles to a given manifold. Figure 1 shows a few examples. Just over a decade ago, Perelman posted the outlines of a proof of the Geometrization Theorem on the ArXiv [56, 57], and with his work and that of others it is now known that all 3–manifolds decompose ...
متن کامل