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

Abstract

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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 standard spherical isometric folding f s defined by f s ( x , y , z ) = ( x , y , | z | ) .

How to cite

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Breda, 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

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  1. Breda, A. M. d'Azevedo, {Isometric Foldings}, PhD Thesis, University of Southampton, U.K. (1989). (1989) 
  2. Breda, A. M. d'Azevedo, A class of tilings of S 2 , Geometriae Dedicata 44 (1992), 241-253. (1992) MR1193117
  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. (2004) MR2093177
  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. (2005) MR2164062
  5. Breda, A. M. d'Azevedo, Santos, A. F., 10.32917/hmj/1166642302, Hiroshima Math. J. 36 (2006), 235-288. (2006) MR2259739DOI10.32917/hmj/1166642302
  6. Hirsch, M., {Differential Topology}, Graduate Texts in Math, 33 Springer-Verlag, New York (1976). (1976) Zbl0356.57001MR0448362
  7. 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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