International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 1, Pages 91-97
doi:10.1155/IJMMS.2005.91

Image sets of folding surfaces

Abstract

Isometric foldings are a special class of length-preserving maps of Riemannian manifolds and were initially studied by S. Robertson. For an explanation of their topological and combinatorial properties, see the related works of Ana Breda, Altino Santos, M. El-Ghoul, and E. M. Elkholy. Here, we explore some properties of the singular set and describe the image set of planar, spherical, and hyperbolic foldings.