Linear combinations of hypersurfaces in hyperbolic space
type: Item
instance of: scholarly article
title: Linear combinations of hypersurfaces in hyperbolic space
zbMATH Open document ID: 1276.53065
author: Gil Solanes
author: Eduardo Gallego
author: Eberhard Teufel
published in: Monatshefte für Mathematik
publication date: 2013-03-18T00:00:00Z
review text: The authors introduce and investigate linear combinations of hypersurfaces in hyperbolic space. They use some linear structure in the space of horosphere. They define a scalar multiplication, the \(h\)-dilation, and the two additions, the sum and the harmonic sum. These new constructions are invariant with respect to the group of hyperbolic motions.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 52A55
zbMATH DE Number: 6146029
zbMATH Keywords: hyperbolic space
zbMATH Keywords: Minkowski addition
zbMATH Keywords: horospheres
zbMATH Keywords: convex sets
MaRDI profile type: Publication
full work available at URL: s00605-012-0405-x
OpenAlex ID: W1984881649
cites work: Steiner’s formulae on a general 𝑆ⁿ⁺¹
cites work: Curvature Measures
cites work: Barbier's Theorem in the Lobachevski Plane
cites work: Asymptotic behaviour of \(\lambda\)-convex sets in the hyperbolic plane
cites work: Width of convex bodies in spaces of constant curvature
cites work: SINGULARITIES OF HYPERBOLIC GAUSS MAPS
cites work: The geometry of canal surfaces and the length of curves in de Sitter space
cites work: Linear combinations of convex hypersurfaces in non-Euclidean geometry
cites work: On the addition of convex sets in the hyperbolic plane
cites work: Support function and hyperbolic plane
cites work: Foundations of Hyperbolic Manifolds
cites work: Horocycles and convex sets in hyperbolic plane
cites work: Horospheres and Convex Bodies in Hyperbolic Space
cites work: Hypersurfaces in \(H^n\) and the space of its horospheres
cites work: Q5287551
cites work: A generalization of Steiner’s formulae
DOI: 10.1007/S00605-012-0405-X
description: scientific article; zbMATH DE number 6146029