2024-03-29T08:15:28Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/696422022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Projections of surfaces in the hyperbolic space to hyperhorospheres and hyperplanesIzumiya, ShyuichiTari, FaridBifurcation setscontoursLegendrian dualityprojectionsprofileshyperbolic spacesingularitiesde Sitter spacelightcone.410We 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69642info:doi/10.14943/83983https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69642/1/pre833.pdfHokkaido University Preprint Series in Mathematics8331192007-03-08engpublisher