Projections of surfaces in the hyperbolic space to hyperhorospheres and hyperplanes
Projections of surfaces in the hyperbolic space to hyperhorospheres and hyperplanes
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DOI：
10.4171/rmi/559
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发表时间：
2007-03
期刊：
影响因子：
--
通讯作者：
S. Izumiya;F. Tari
中科院分区：
文献类型：
--
作者：
S. Izumiya;F. Tari
本文研究了双曲空间中到超球面和超平面的正交投影。我们更详细地讨论了$H^3_+(-1)$中嵌入曲面$M$的情况。我们研究了$M$到角球和平面的投影的一般奇异性。我们给出了这些奇点的几何特征，并证明了关于投影族分支集的对偶结果。我们还证明了Koendrink型定理，该定理根据曲面的轮廓曲率和法截面曲率给出了曲面曲率。
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.