The convex real projective orbifolds with radial or totally geodesic ends: a survey of some partial results
The convex real projective orbifolds with radial or totally geodesic ends: a survey of some partial results
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具有径向或全测地线末端的凸实射影轨道折叠：一些部分结果的调查
DOI：
10.1090/conm/696/14016
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Suhyoung Choi
中科院分区：
文献类型：
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作者：
Suhyoung Choi
一个真实的射影轨道褶皱有一个径向端点，如果端点的邻域由射影测地线划分，这些测地线发展成终止于一个公共点的测地线。它有一个全测地的结束，如果结束可以完成有全测地的边界。
本文的目的是公布一些部分结果。真实的射影结构有时允许对真实的射影结构的参数进行变形。我们将证明一个具有径向或全测地端点的Orbifold $\mathcal{O}$上的凸真实的射影结构的变形空间与\[ Hom（\pi_{1}（\mathcal{O}），PGL（n+1，\mathbb {R}））/PGL（n +1，\mathbb{R}）的相应子集的层的开子空间的并之间的同胚。最后，我们将讨论适当的开放性和封闭性。一类具有广义容许端点的orbifold上的（严格）凸真实的射影结构。
A real projective orbifold has a radial end if a neighborhood of the end is foliated by projective geodesics that develop into geodesics ending at a common point. It has a totally geodesic end if the end can be completed to have the totally geodesic boundary.
The purpose of this paper is to announce some partial results. A real projective structure sometimes admits deformations to parameters of real projective structures. We will prove a homeomorphism between the deformation space of convex real projective structures on an orbifold $\mathcal{O}$ with radial or totally geodesic ends with various conditions with the union of open subspaces of strata of the corresponding subset of \[ Hom(\pi_{1}(\mathcal{O}), PGL(n+1, \mathbb{R}))/PGL(n+1, \mathbb{R}).\] Lastly, we will talk about the openness and closedness of the properly (resp. strictly) convex real projective structures on a class of orbifold with generalized admissible ends.