论文标题
非欧几里得拉瓜几何和非圆网
Non-Euclidean Laguerre geometry and incircular nets
论文作者
论文摘要
经典的（欧几里得）拉瓜几何学研究以欧几里得空间中定向的超平面，定向超球体及其定向的接触。我们描述了如何将其推广到任意的Cayley-Klein空间，特别是双曲线和椭圆形空间，并研究Laguerre转换的相应组。我们介绍了谎言的几何形状，并描述了如何以亚地位的形式获得这些laguerre几何形状。作为二维谎言和拉瓜几何形状的应用，我们研究了不圆网的特性。
Classical (Euclidean) Laguerre geometry studies oriented hyperplanes, oriented hyperspheres, and their oriented contact in Euclidean space. We describe how this can be generalized to arbitrary Cayley-Klein spaces, in particular hyperbolic and elliptic space, and study the corresponding groups of Laguerre transformations. We give an introduction to Lie geometry and describe how these Laguerre geometries can be obtained as subgeometries. As an application of two-dimensional Lie and Laguerre geometry we study the properties of incircular nets.
