Displaying similar documents to “Conformal invariants in two dimensions. [I.]”

Uniqueness of the stereographic embedding

Michael Eastwood (2014)

Archivum Mathematicum

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The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.

Application of spaces of subspheres to conformal invariants of curves and canal surfaces

Rémi Langevin, Jun O'Hara, Shigehiro Sakata (2013)

Annales Polonici Mathematici

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We review some techniques from the Möbius geometry of curves and surfaces in the 3-sphere, consider canal surfaces using their characteristic circles, and express the conformal curvature, and conformal torsion, of a vertex-free space curve in terms of its corresponding curve of osculating circles, and osculating spheres, respectively. We accomplish all of this strictly within the framework of Möbius geometry, and compare our results with the literature. Finally, we show how our formulation...