| Title:
|
On deformations of spherical isometric foldings (English) |
| Author:
|
Breda, Ana M. |
| Author:
|
Santos, Altino F. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
149-159 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $f_s(x,y,z)=(x,y,|z|)$. (English) |
| Keyword:
|
isometric foldings |
| Keyword:
|
edge-to-edge spherical tilings |
| Keyword:
|
homotopy |
| MSC:
|
52B05 |
| MSC:
|
52C20 |
| MSC:
|
55P10 |
| MSC:
|
57Q55 |
| idZBL:
|
Zbl 1224.52028 |
| idMR:
|
MR2595079 |
| . |
| Date available:
|
2010-07-20T16:23:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140558 |
| . |
| Reference:
|
[1] Breda, A. M. d'Azevedo: {Isometric Foldings}.PhD Thesis, University of Southampton, U.K. (1989). |
| Reference:
|
[2] Breda, A. M. d'Azevedo: {A class of tilings of $S^2$}.Geometriae Dedicata 44 (1992), 241-253. MR 1193117 |
| Reference:
|
[3] Breda, A. M. d'Azevedo, Santos, A. F.: Dihedral $f$-tilings of the sphere by spherical triangles and equiangular well centered quadrangles.Beiträge Algebra Geometrie 45 (2004), 447-461. MR 2093177 |
| Reference:
|
[4] Breda, A. M. d'Azevedo, Santos, A. F.: Dihedral $f$-tilings of the sphere by rhombi and triangles.Discrete Math. Theoretical Computer Sci. 7 (2005), 123-140. MR 2164062 |
| Reference:
|
[5] Breda, A. M. d'Azevedo, Santos, A. F.: {Dihedral $f$-tilings of the sphere by triangles and well centered quadrangles}.Hiroshima Math. J. 36 (2006), 235-288. MR 2259739, 10.32917/hmj/1166642302 |
| Reference:
|
[6] Hirsch, M.: {Differential Topology}.Graduate Texts in Math, 33 Springer-Verlag, New York (1976). Zbl 0356.57001, MR 0448362 |
| Reference:
|
[7] Robertson, S. A.: {Isometric folding of riemannian manifolds}.Proc. Royal Soc. Edinb. Sect. A 79 (1977), 275-284. Zbl 0418.53016, MR 0487893 |
| . |
