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November, 2008 Projections of hypersurfaces in the hyperbolic space to hyperhorospheres and hyperplanes
Shyuichi Izumiya , Farid Tari
Rev. Mat. Iberoamericana 24(3): 895-920 (November, 2008).


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 characterizations of these singularities and prove duality results concerning the bifurcation sets of the families of projections. We also prove Koenderink type theorems that give the curvature of the surface in terms of the curvatures of the profile and the normal section of the surface.


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Shyuichi Izumiya . Farid Tari . "Projections of hypersurfaces in the hyperbolic space to hyperhorospheres and hyperplanes." Rev. Mat. Iberoamericana 24 (3) 895 - 920, November, 2008.


Published: November, 2008
First available in Project Euclid: 9 December 2008

zbMATH: 1170.53011
MathSciNet: MR2490202

Primary: 53A35 , 58K05

Keywords: bifurcation sets , contours , de Sitter space , Hyperbolic space , Legendrian duality , lightcone , profiles , projections , singularities

Rights: Copyright © 2008 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.24 • No. 3 • November, 2008
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