Factorizations of the Conformal Villarceau Motion
Daren Thimm -- University of Innsbruck
Rational conformal motions can be described by polynomials over the even sub-algebra of a geometric algebra having a real norm polynomial. These polynomials are called spinor polynomials and factorizing them corresponds to splitting the rational motion they describe into sub-motions of lower degree. Generic spinor polynomials have a finite amount of factorizations. Examples of polynomials with an infinte amount of factorizations are very rare. In this abstract we investigate one such special case of a spinor polynomial namely the conformal Villarceau motion. We aim to give an intuitive introduction to its construction, calculate its factorizations and interpret them geometrically.