Horospheres and Convex Bodies in n-Dimensional Hyperbolic Space

被引：0

作者：

E. Gallego

A. M. Naveira

G. Solanes

机构：

[1] Universitat Autònoma de Barcelona,Departament de Matemàtiques

[2] Departamento de Geometría y Topología,Facultad de Matemáticas

来源：

Geometriae Dedicata | 2004年 / 103卷

关键词：

convex set; -convex set; horocycle; horosphere; hyperbolic space; volume;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In n-dimensional Euclidean space, the measure of hyperplanes intersecting a convex domain is proportional to the (n−2)-mean curvature integral of its boundary. This question was considered by Santaló in hyperbolic space. In non-Euclidean geometry the totally geodesic hypersurfaces are not always the best analogue to linear hyperplanes. In some situations horospheres play the role of Euclidean hyperplanes.

引用

页码：103 / 114

页数：11

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