# On deformations of spherical isometric foldings

Ana M. Breda; Altino F. Santos

Czechoslovak Mathematical Journal (2010)

- Volume: 60, Issue: 1, page 149-159
- ISSN: 0011-4642

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topBreda, Ana M., and Santos, Altino F.. "On deformations of spherical isometric foldings." Czechoslovak Mathematical Journal 60.1 (2010): 149-159. <http://eudml.org/doc/37997>.

@article{Breda2010,

abstract = {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 standard spherical isometric folding $f_s$ defined by $f_s(x,y,z)=(x,y,|z|)$.},

author = {Breda, Ana M., Santos, Altino F.},

journal = {Czechoslovak Mathematical Journal},

keywords = {isometric foldings; edge-to-edge spherical tilings; homotopy; isometric folding; edge-to-edge spherical tiling; homotopy},

language = {eng},

number = {1},

pages = {149-159},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On deformations of spherical isometric foldings},

url = {http://eudml.org/doc/37997},

volume = {60},

year = {2010},

}

TY - JOUR

AU - Breda, Ana M.

AU - Santos, Altino F.

TI - On deformations of spherical isometric foldings

JO - Czechoslovak Mathematical Journal

PY - 2010

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 60

IS - 1

SP - 149

EP - 159

AB - 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 standard spherical isometric folding $f_s$ defined by $f_s(x,y,z)=(x,y,|z|)$.

LA - eng

KW - isometric foldings; edge-to-edge spherical tilings; homotopy; isometric folding; edge-to-edge spherical tiling; homotopy

UR - http://eudml.org/doc/37997

ER -

## References

top- Breda, A. M. d'Azevedo, {Isometric Foldings}, PhD Thesis, University of Southampton, U.K. (1989). (1989)
- Breda, A. M. d'Azevedo, A class of tilings of ${S}^{2}$, Geometriae Dedicata 44 (1992), 241-253. (1992) MR1193117
- 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. (2004) MR2093177
- 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. (2005) MR2164062
- Breda, A. M. d'Azevedo, Santos, A. F., 10.32917/hmj/1166642302, Hiroshima Math. J. 36 (2006), 235-288. (2006) MR2259739DOI10.32917/hmj/1166642302
- Hirsch, M., {Differential Topology}, Graduate Texts in Math, 33 Springer-Verlag, New York (1976). (1976) Zbl0356.57001MR0448362
- Robertson, S. A., {Isometric folding of riemannian manifolds}, Proc. Royal Soc. Edinb. Sect. A 79 (1977), 275-284. (1977) Zbl0418.53016MR0487893

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