论文标题
Cayley-Klein空间中的极性品种
Polar Varieties in Cayley-Klein Spaces
论文作者
论文摘要
在本文中，我们在分析框架中介绍了Cayley-Klein空间的任意子空间的总极性的概念。我们表明，子空间的所有总体杆的集合都是舒伯特品种。总极的概念给出了一个定义子空间与空间的绝对图形相切。通过指定切线，切线锥，然后定义球体。球体的定义不取决于空间的度量。事实证明，Cayley-Klein空间的每一个反射，由两个彼此之间的两个子空间定义，都是空间的运动。另一方面，尺寸n的Cayley-Klein空间中的每一个运动都是最多的n+1反射的产物。
In this paper, we introduce the notion of a total polar for an arbitrary subspace of a Cayley-Klein space in an analytical framework. We show that the set of all total polars of a subspace is a Schubert variety. The notion of total polar gives a definition for a subspace to be tangent to the absolute figure of the space. By specifying tangent lines, tangent cones and then spheres are defined. This definition of the sphere does not depend on the metric of the space. It is proved that every reflection of a Cayley- Klein space, defined by two subspaces which are total polar to each other, is a motion of the space. On the other hand, each motion in a Cayley-Klein space of dimension n is a product of at most n+1 reflections in point-hyperplane pairs.
