论文标题
代数的几何形状
Geometry over algebras
论文作者
论文摘要
我们研究由除划分外的真实代数上的线性空间上的遗传形式产生的几何结构。我们的重点是双重数字，拆分复合数和分配标记。采用相应的几何结构来描述双曲机平面，欧几里得平面和圆形$ 2 $ -SPHERE中定向的大地测量空间。我们还引入了这些空间之间的简单自然的几何跃迁。最后，我们提出了双曲线双盘的投影模型，即两个双曲盘的riemannian产品。
We study geometric structures arising from Hermitian forms on linear spaces over real algebras beyond the division ones. Our focus is on the dual numbers, the split-complex numbers, and the split-quaternions. The corresponding geometric structures are employed to describe the spaces of oriented geodesics in the hyperbolic plane, the Euclidean plane, and the round $2$-sphere. We also introduce a simple and natural geometric transition between these spaces. Finally, we present a projective model for the hyperbolic bidisc, that is, the Riemannian product of two hyperbolic discs.
