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Hokkaido University Preprint Series in Mathematics >
Projections of surfaces in the hyperbolic space along horocycles
| Title: | Projections of surfaces in the hyperbolic space along horocycles |
| Authors: | Izumiya, Shyuichi Browse this author | | Tari, Farid Browse this author |
| Keywords: | Bifurcation sets | | contours | | Legendrian duality | | projections | | profiles | | hyperbolic space | | singularities | | de Sitter space | | lightcone |
| Issue Date: | 9-Jan-2008 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 887 |
| Start Page: | 1 |
| End Page: | 22 |
| Abstract: | We study in this paper orthogonal projections of embedded surfaces $M$ in $H^3_+(-1)$ along horocycles to planes. The singularities of the projections capture the extrinsic geometry of $M$ related to the lightcone Gauss map. We give geometric characterisations of these singularities and prove a Koenderink type theorem which relates the hyperbolic curvature of the surface to the curvature of the profile and of the normal section of the surface. We also prove duality results concerning the bifurcation set of the family of projections. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69696 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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