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# Projections of surfaces in the hyperbolic space along horocycles

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 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