PG（3，R）的旋转展开、旋转平行性和定向平行性
Rotational spreads and rotational parallelisms and oriented parallelisms of PG(3,R)
摘要：
我们介绍了有向线的拓扑平行性（简称为有向平行性）。PG（3，R）上的每一个拓扑平行性（线）引起的平行性定向线，但我们表明，即使是最均匀的平行性定向线以外的克利福德平行不一定会出现这种方式。事实上，我们确定所有的平行的两种类型，承认一个可约SO（3）-行动。只有克利福德平行承认一个更大的群体令人惊讶的是，事实证明，有更多的定向平行这种比普通的平行。特别地，我们证明了Betten和Riesinger构造的SO（3）不变的普通平行性是唯一与此群作用相容的平行性.我们还研究了旋转Betten蔓延在这个建设和他们的自同构。（定向）平行性的自同构群总是SO（3），无论非正则扩散的自同构群有多大。同构类型的并行性远远多于传播类型。
英文摘要：
We introduce topological parallelisms of oriented lines (briefly called oriented parallelisms). Every topological parallelism (of lines) on PG(3,R) gives rise to a parallelism of oriented lines, but we show that even the most homogeneous parallelisms of oriented lines other than the Clifford parallelism do not necessarily arise in this way. In fact we determine all parallelisms of both types that admit a reducible SO(3)-action. Only the Clifford parallelism admits a larger group Surprisingly, it turns out that there are far more oriented parallelisms of this kind than ordinary parallelisms. In particular, we show that the SO(3)-invariant ordinary parallelisms constructed by Betten and Riesinger are the only ones compatible with this group action. We also study the rotational Betten spreads used in this construction and their automorphisms. The automorphism group of the (oriented) parallelisms is always SO(3), no matter how large the automorphism group of the non-regular spread is. There are far more isomorphism types of parallelisms than types of spreads.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
