Abstract
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.
Citation
Shyuichi Izumiya. Masatomo Takahashi. Farid Tari. "Folding maps on spacelike and timelike surfaces and duality." Osaka J. Math. 47 (3) 839 - 862, September 2010.
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