Geodesic
On deformations of spherical isometric foldings
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 149-159.

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The behavior of special classes of isometric foldings of the Riemannian sphere $S^2$ under the action of angular conformal deformations is considered. It is shown that within these classes any isometric folding is continuously deformable into the {\it standard} spherical isometric folding $f_s$ defined by $f_s(x,y,z)=(x,y,|z|)$.
Classification : 52B05, 52C20, 55P10, 57Q55
Keywords: isometric foldings; edge-to-edge spherical tilings; homotopy 
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     author = {Breda, Ana M. and Santos, Altino F.},
     title = {On deformations of spherical isometric foldings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {149--159},
     publisher = {mathdoc},
     volume = {60},
     number = {1},
     year = {2010},
     mrnumber = {2595079},
     zbl = {1224.52028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010__60_1_a12/}
}
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Breda, Ana M.; Santos, Altino F. On deformations of spherical isometric foldings. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 149-159. http://geodesic.mathdoc.fr/item/CMJ_2010__60_1_a12/