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Hokkaido University Preprint Series in Mathematics >
Projections of surfaces in the hyperbolic space to hyperhorospheres and hyperplanes
| Title: | Projections of surfaces in the hyperbolic space to hyperhorospheres and hyperplanes |
| 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: | 8-Mar-2007 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 833 |
| Start Page: | 1 |
| End Page: | 19 |
| Abstract: | We study in this paper orthogonal projections in a hyperbolic space to hyperhorospheres and hyperplanes. We deal in more details with the case of embedded surfaces $M$ in $H^3_+(-1)$. We study the generic singularities of the projections of $M$ to horospheres and planes. We give geometric characterisations of these singularities and prove duality results concerning the bifurcation sets of the families of projections. We also prove Koendrink type theorems that give the curvature of the surface in terms of the curvatures of the profile and the normal section of the surface. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69642 |
| 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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