Translational and great Darboux cyclides
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Publication:6507432
arXiv1306.1917MaRDI QIDQ6507432
Author name not available (Why is that?)
Abstract: A surface that is the pointwise sum of circles in Euclidean space is either coplanar or contains no more than 2 circles through a general point. A surface that is the pointwise product of circles in the unit-quaternions contains either 2, 3, 4, or 5 circles through a general point. A surface in a unit-sphere of any dimension that contains 2 great circles through a general point contains either 4, 5, 6, or infinitely many circles through a general point. These are some corollaries from our classification of translational and great Darboux cyclides. We use the combinatorics associated to the set of low degree curves on such surfaces modulo numerical equivalence.
Has companion code repository: https://github.com/niels-lubbes/orbital
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