Department of Mathematics, Graduate School of Science, Osaka University
Osaka Journal of Mathematics
We study the reflectional symmetry of a generically embedded 2-dimensional surface M in the hyperbolic or de Sitter 3-dimensional spaces. This symmetry is picked up by the singularities of folding maps that are defined and studied here. We also define the evolute and symmetry set of M and prove duality results that relate them to the bifurcation sets of the family of folding maps.