2023-03-27T04:37:57Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696962022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Projections of surfaces in the hyperbolic space along horocyclesIzumiya, ShyuichiTari, Faridopen accessBifurcation setscontoursLegendrian dualityprojectionsprofileshyperbolic spacesingularitiesde Sitter spacelightcone410We 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.Department of Mathematics, Hokkaido University2008-01-09engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84037http://hdl.handle.net/2115/6969610.14943/84037Hokkaido University Preprint Series in Mathematics887122https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69696/1/pre887.pdfapplication/pdf243.61 KB2008-01-09