The concept of spine geometry over a polar Grassmann space is introduced. We determine conditions under which the structure of lines together with a binary coplanarity relation is a sufficient system of primitive notions for polar spine spaces. These assumptions also allow to characterize polar spine spaces in terms of the binary relation of being in one pencil of lines.

中文翻译：

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极地脊柱空间线上的几何

介绍了极地格拉斯曼空间上的脊椎几何概念。我们确定条件，在这些条件下，线的结构与二进制共面关系一起成为极地脊柱空间的原始概念的足够系统。这些假设还允许根据一条直线中的二元关系来描述极地脊柱空间。