Hokkaido University | Library | HUSCAP Advanced Search 言語 日本語 English

# Projections of surfaces in the hyperbolic space to hyperhorospheres and hyperplanes

Files in This Item:
 pre833.pdf 258.84 kB PDF View/Open
 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 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