Isotropic Möbius Geometry and i-M Circles on Singular Isotropic Cyclides

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9213)


The Möbius geometry of \({\mathbb R}^3\) has an isotropic counterpart in \(\mathbb {R}^{3}_{++0}\). We describe the isotropic Möbius model of surfaces in \(\mathbb {R}^{3}_{++0}\) 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 \(\mathbb {R}^{3}_{++0}\) to isotropic cyclides with real singularities, containing up to 4 such families.



We would like to thank Rimvydas Krasauskas, Niels Lubbes, Torgunn Karoline Moe, and Severinas Zubė for our discussions about and their feedback on this paper. We would also like to thank the reviewers for their constructive comments.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Applied MathematicsSINTEF ICTOsloNorway

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