Galilei Laguerre Geometry and Rational Circular Ooset Surfaces

In this paper the Laguerre geometry of three-dimensional Galilei space, that is, the geometry of oriented planes and cycles of an aane Cayley-Klein space with absolute line and two conjugate complex absolute points on it, is studied. Several diierent models are presented: A cyclographic model and an isotropic model together with their duals and an interpretation in terms of geometrical optics of Galilei space. We also have a closer look on Laguerre transformations. Galilei geometry arises naturally in the context of rational surfaces which possess rational circular ooset surfaces, and it can also be used for modeling rational circular ooset surfaces, e. g., with Galilei cyclides.