Width and breadth for convex bodies in Riemannian manifolds
type: Item
instance of: scholarly article
title: Width and breadth for convex bodies in Riemannian manifolds
zbMATH Open document ID: 0726.52001
DOI: 10.1007/BF01191885
published in: Archiv der Mathematik
publication date: 1992-01-01T00:00:00Z
review text: Bodies of constant width W in a Riemannian manifold \(M^ n\) were considered recently in a few papers. The width itself was not introduced there. The bodies were defined by means of the property that each longest geodesic within such a body orthogonal to its boundary at one of its ends has the same length W. Here, we define a width of a convex body in \(M^ n\) and show that the body is of constant width if and only if this newly introduced width is constant.
Mathematics Subject Classification ID: 52A05
Mathematics Subject Classification ID: 53C20
zbMATH DE Number: 4198920
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: width of a convex body
zbMATH Keywords: constant width
author: B. V. Dekster
MaRDI profile type: Publication
Wikidata QID: Q115393939
cites work: Q5848673
cites work: Q5674080
cites work: TRANSNORMAL SYSTEMS
cites work: CONVEX SETS IN RIEMANNIAN SPACES OF NON-NEGATIVE CURVATURE
cites work: On the structure of complete manifolds of nonnegative curvature
cites work: Q3357035
cites work: In- and circumcenters of manifolds of constant width
cites work: Q4486209
cites work: Q4288739
cites work: Transnormal hypersurfaces. Generalized constant width for Riemannian manifolds
cites work: Compact two-transnormal hypersurfaces in a space of constant curvature
full work available at URL: https://doi.org/10.1007/bf01191885
OpenAlex ID: W1996683675
description: scientific article; zbMATH DE number 4198920