An introduction to the theory of generalized conics and their applications
type: Item
instance of: scholarly article
title: An introduction to the theory of generalized conics and their applications
zbMATH Open document ID: 1217.53078
published in: Journal of Geometry and Physics
publication date: 2011-03-14T00:00:00Z
review text: Let \(\Gamma\) be a fixed point set in a Euclidean space. A generalized conic is a set of points with the same average distance from \(\Gamma\). In this paper, the authors give a process to construct convex bodies which are invariant under a fixed subgroup of the orthogonal group in the Euclidean space, using generalized conics. As an application, the authors consider the holonomy group of Riemannian manifolds and prove some metrizable results. In particular, they prove that there are eight classes of manifolds equipped with an invariant smooth collection of Minkowski functionals on the tangent spaces, called Berwalds spaces in a general sense.
reviewed by: Shaoqiang Deng
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 58B20
Mathematics Subject Classification ID: 51B20
Mathematics Subject Classification ID: 52A20
zbMATH DE Number: 5865473
zbMATH Keywords: Minkowski functionals
zbMATH Keywords: Finsler manifolds
zbMATH Keywords: Berwald manifolds
author: Csaba Vincze
author: Ábris Nagy
MaRDI profile type: Publication
full work available at URL: j.geomphys.2010.12.003
OpenAlex ID: W1974689301
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DOI: 10.1016/J.GEOMPHYS.2010.12.003
description: scientific article; zbMATH DE number 5865473