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Application of spaces of subspheres to conformal invariants of curves and canal surfaces. (English) Zbl 1291.53009
A “canal surface” in the conformal \(3\)-sphere is a surface that envelops a \(1\)-parameter family of spheres. Alternatively, a canal surface can be characterized by the fact that one family of curvature lines consists of circular arcs. The authors discuss both points of view to elucidate the geometric relations between these two descriptions of canal surfaces, in particular, between the invariants of the corresponding curves in the space of spheres and the space of circles, respectively.
MSC:
53A30 Conformal differential geometry (MSC2010)
53B25 Local submanifolds
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