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SINGULARITIES OF EVOLUTES OF HYPERSURFACES IN HYPERBOLIC SPACE

Published online by Cambridge University Press:  27 May 2004

Shyuichi Izumiya ,
Donghe Pei  and
Masatomo Takahashi
Shyuichi Izumiya
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan (izumiya@math.sci.hokudai.ac.jp)
Donghe Pei
Affiliation:
Department of Mathematics, Northeast Normal University, Changchun 130024, People's Republic of China (northlcd@public.cc.jl.cn; pei@math.sci.hokudai.ac.jp)
Masatomo Takahashi
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan (takahashi@math.sci.hokudai.ac.jp)
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Abstract

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We study the differential geometry of hypersurfaces in hyperbolic space. As an application of the theory of Lagrangian singularities, we investigate the contact of hypersurfaces with families of hyperspheres or equidistant hyperplanes.

AMS 2000 Mathematics subject classification: Primary 53A35. Secondary 58C27

Keywords

hypersphereequidistant hyperplanehyperbolic (de Sitter) evolutehyperbolic timelike (spacelike) height functionLagrangian singularities
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 47 , Issue 1 , February 2004 , pp. 131 - 153
Copyright
Copyright © Edinburgh Mathematical Society 2004