论文标题
无限$ \ {3,7 \} $ - $ \ mathbb {h}^3 $
Infinite $\{3,7\}$-surface in $\mathbb{H}^3$
论文作者
论文摘要
具有大型对称群体的对象一直是许多数学家的兴趣。几何学中的一个经典问题是，是否具有某些几何特征的表面（例如完整性，曲率等）是否可以嵌入$ \ mathbb {r}^3。$在最近的一篇论文中，Lee构建了一个无限$ \ {3,7 \ \} $ - 在$ \ mathbb {r} r}^3 $ in and and and prims in the and primes and primiss and primiss and primiss and primiss and primiss and primiss and Infims and Infims， $ \ mathbb {r}^3 $，是克莱因四分之一的封面。尽管Lee的构造表明，此类构造自我交流在$ \ Mathbb {r}^3 $中，但并未证明也不能反驳嵌入的可能性。在本文中，我们探讨了三个klein Quartic属或其覆盖物的可能嵌入在双曲线空间中。
Objects with large symmetry groups have been an interest for many mathematicians. A classical question in geometry is whether a surface with certain geometric features, such as completeness, curvature, etc..., can embed in $\mathbb{R}^3.$ In a recent paper, Lee constructs an infinite $\{3,7\}$-surface in $\mathbb{R}^3$ by gluing together prisms and antiprisms, in an attempt to find a periodic surface in $\mathbb{R}^3$ that is cover of Klein's quartic. While Lee's construction shows that such construction self-intersects in $\mathbb{R}^3$, it does not prove nor disprove the possibility of an embedding. In this paper, we explore a possible embedding of the genus three Klein's quartic, or its cover, in hyperbolic space.
