Galilei Laguerre geometry and rational circular offset surfaces (Q1267326)

The authors study the Laguerre geometry of the three-dimensional Galilei space. They investigate special models of this geometry (a cyclographic and an isotropic model with their duals) and its relevance for Laguerre transformations. These methods are used to construct ``rational circular offset surfaces \(\Psi\)'' of special given rational surfaces \(\Phi\): There the offset surface \(\Psi\) is generated by the Euclidean offset curves of the slices of \(\Phi\) in the parallel planes of a parallel bundle. The resulting surface \(\Psi\) then is an offset of \(\Phi\) with respect to a suitable chosen Galilei space and belongs to its Laguerre geometry. Then the authors give examples of rational circular offset surfaces (Galilei cyclides) and use them to model Galilei canal surfaces.