Folding maps on spacelike and timelike surfaces and duality
Preprint Series # 853
Izumiya, Shyuichi and Takahashi, Masatomo and Tari, Farid Folding maps on spacelike and timelike surfaces and duality. (2007);
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.
|Uncontrolled Keywords:||Bifurcation sets, duality, evolute, folding maps, height functions, hyperbolic space, de Sitter space, singularities, symmetry set.|
|Subjects:||53-xx DIFFERENTIAL GEOMETRY|