Isotropic Möbius geometry and i-M circles on singular isotropic cyclides

Abstract

The Möbius geometry of ℝ3 has an isotropic counterpart in ℝ3++0. We describe the isotropic Möbius model of surfaces in ℝ3++0 and show how the degree of a surface changes under i-M inversions while the number of families of i-M circles remain constant. This gives us a generalization of the classification of families of lines and i-M circles on quadratic surfaces in ℝ3++0 to isotropic cyclides with real singularities, containing up to 4 such families.