A new metric on spherical f-tilings

Data
2015-04
Autores
Santos, Altino
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Mathematical Association of America
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Resumo
The continuous deformation of any spherical isometric folding into the standard spherical folding, fs, defined by fs(x, y, z) = (x, y, |z|), remains an open problem since 1989. Some relations between deformation of spherical isometric foldings and deformation of spherical f-tilings are analyzed, as they are closely related. The natural way to deform f-tilings is based on the Hausdorff metric on compact sets. However this metric does not induce a continuous deformation on its associated isometric foldings. A new metric on spherical f-tilings will be approached and a new contribution to the deformation of isometric foldings (via deformation of f-tilings) will be given.
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Continuous deformation , isometric folding , metric , spherical tiling
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