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Projections of surfaces in the hyperbolic space to hyperhorospheres and hyperplanes

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83983

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

Submitter: 数学紀要登録作業用

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