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Projections of surfaces in the hyperbolic space along horocycles

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84037

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
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

Submitter: 数学紀要登録作業用

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