Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Drumm, Todd A."'
In the early 1980's Margulis startled the world by showing the existence of proper affine actions of free groups on 3-space, answering a provocative and suggestive question Milnor posed in 1977. In this paper we discuss the historical background moti
Externí odkaz:
http://arxiv.org/abs/2002.09520
Let $\mathbf{E}$ be a flat Lorentzian space of signature $(2, 1)$. A Margulis space-time is a noncompact complete flat Lorentzian $3$-manifold $\mathbf{E}/\Gamma$ with a free holonomy group $\Gamma$ of rank $\mathbf{g}, \mathbf{g} \geq 2$. We conside
Externí odkaz:
http://arxiv.org/abs/1710.09162
Bisectors are equidistant hypersurfaces between two points and are basic objects in a metric geometry. They play an important part in understanding the action of subgroups of isometries on a metric space. In many metric geometries (spherical, Euclide
Externí odkaz:
http://arxiv.org/abs/1608.07342
A Margulis spacetime is a complete flat Lorentzian 3-manifold M with free fundamental group. Associated to M is a noncompact complete hyperbolic surface S homotopy-equivalent to M. The purpose of this paper is to classify Margulis spacetimes when S i
Externí odkaz:
http://arxiv.org/abs/1501.04535
We develop the Lorentzian geometry of a crooked halfspace in 2+1-dimensional Minkowski space. We calculate the affine, conformal and isometric automorphism groups of a crooked halfspace, and discuss its stratification into orbit types, giving an expl
Externí odkaz:
http://arxiv.org/abs/1211.4177
The following are notes on the geometry of the bidisk. In particular, we examine the properties of equidistant surfaces in the bidisk.
Comment: 12 pages, 4 figures. Accepted for publication in Geometriae Dedicata
Comment: 12 pages, 4 figures. Accepted for publication in Geometriae Dedicata
Externí odkaz:
http://arxiv.org/abs/1206.1342
A Margulis spacetime is a complete affine 3-manifold M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S. We show that every Margulis spacetime is orientable, even though S may be
Externí odkaz:
http://arxiv.org/abs/1107.2862
Publikováno v:
Geometry & Topology 14 (2010), 1355-1382
Associated to every complete affine 3-manifold M with nonsolvable fundamental group is a noncompact hyperbolic surface S. We classify such complete affine structures when Sigma is homeomorphic to a three-holed sphere. In particular, for every such co
Externí odkaz:
http://arxiv.org/abs/0907.0690
Publikováno v:
Contemporary Mathematics {\bf 510} (2009), 61--70
This paper applies the authors' forthcoming work, "Affine deformations of a three-holed sphere" in Lorentzian geometry to prove a result in hyperbolic geometry. Namely, an infinitesimal deformation of a hyperbolic structure of a three-holed sphere wh
Externí odkaz:
http://arxiv.org/abs/0907.0680
Publikováno v:
in "Recent Developments in Pseudo-Riemannian Geometry", European Mathematical Society, (2008), 179--230
The Einstein universe is the conformal compactification of Minkowski space. It also arises as the ideal boundary of anti-de Sitter space. The purpose of this article is to develop the synthetic geometry of the Einstein universe in terms of its homoge
Externí odkaz:
http://arxiv.org/abs/0706.3055