Dept. Math, Hokkaido Univ. EPrints Server

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);

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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.

Item Type:Preprint
Additional Information:60
Uncontrolled Keywords:Bifurcation sets, duality, evolute, folding maps, height functions, hyperbolic space, de Sitter space, singularities, symmetry set.
Subjects:53-xx DIFFERENTIAL GEOMETRY
ID Code:1706