论文标题
广义线星的PG（3，r）的常规并行性：面向案例
Regular parallelisms on PG(3,R) from generalized line stars: The oriented case
论文作者
论文摘要
使用klein对应关系，Betten和Riesinger用双对象（称为HyperFlockskinging（HFD）线集）描述了Pg（3，R）的常规并行性。在该集合具有尺寸3的特殊情况下，第二个双重化导致更方便的对象，称为概括的线条。后来作者简化了这两种结构。在这里，我们完善了我们简化的方法，以获得定向线的常规并行性的相似结果。结果，我们可以证明，对于我们所说的面向的并行性，与非面向案例相比，存在明显更多的可能性。这些证据需要对投射空间（作为歧管和格子）以及弹丸平面，尤其是翻译平面中的方向进行彻底分析。这是为了根据PG的Klein模型（3，R）来处理定向常规差的连续家庭。事实证明这很微妙。即使是对以面向定向并行性建模的双重对象类别的定义也不是那么明显。
Using the Klein correspondence, regular parallelisms of PG(3,R) have been described by Betten and Riesinger in terms of a dual object, called a hyperflock determining (hfd) line set. In the special case where this set has a span of dimension 3, a second dualization leads to a more convenient object, called a generalized star of lines. Both constructions have later been simplified by the author. Here we refine our simplified approach in order to obtain similar results for regular parallelisms of oriented lines. As a consequence, we can demonstrate that for oriented parallelisms, as we call them, there are distinctly more possibilities than in the non-oriented case. The proofs require a thorough analysis of orientation in projective spaces (as manifolds and as lattices) and in projective planes and, in particular, in translation planes. This is used in order to handle continuous families of oriented regular spreads in terms of the Klein model of PG(3,R). This turns out to be quite subtle. Even the definition of suitable classes of dual objects modeling oriented parallelisms is not so obvious.
