JournalsrmiVol. 24, No. 3pp. 895–920

Projections of hypersurfaces in the hyperbolic space to hyperhorospheres and hyperplanes

  • Shyuichi Izumiya

    Hokkaido University, Sapporo, Japan
  • Farid Tari

    Universidade de São Paulo, São Carlos, Brazil
Projections of hypersurfaces in the hyperbolic space to hyperhorospheres and hyperplanes cover
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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 MM in H+3(1)H^3_+(-1). We study the generic singularities of the projections of MM 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.

Cite this article

Shyuichi Izumiya, Farid Tari, Projections of hypersurfaces in the hyperbolic space to hyperhorospheres and hyperplanes. Rev. Mat. Iberoam. 24 (2008), no. 3, pp. 895–920

DOI 10.4171/RMI/559