The Azimuthal equidistant projection for a Finsler manifold by the exponential map
type: Item
instance of: scholarly article
title: The Azimuthal equidistant projection for a Finsler manifold by the exponential map
zbMATH Open document ID: 1455.53088
author: Nobuhiro Innami
author: Yoe Itokawa
author: Toshiki Kondo
author: Tetsuya Nagano
author: Katsuhiro Shiohama
published in: Pacific Journal of Mathematics
publication date: 2021-01-08T00:00:00Z
review text: Let \((M,F)\) be a geodesically forward complete Finsler manifold endowed with an empty boundary, and \(\exp_p\) be the \(M\)-valued exponential map on \(T_pM\), the tangent space at \(p\in M\). In a few words, let us state some results stated by the authors. They look at the behaviour of two curves \(\tilde{c}(s)\) and \(c(s)=\exp_p(\tilde{c}(s))\) for \(s\in[0,1]\) such that \(\tilde{c}(0)\) belongs to the tangent cut locus of \(p\) and to the first tangent conjugate locus. Then, they seek the relation that exists between the tangent vectors of \(\tilde{c}(s)\) and \(c(s)\) at zero. Also, the authors consider the limit of \(\exp^{-1}_p(c(s))\), as \(s\) approaches zero, for a curve \(c\) such that \(c(0)\) belongs to the cut locus of \(p\).
reviewed by: Mohammed El Aïdi
Mathematics Subject Classification ID: 53C60
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 7291147
zbMATH Keywords: exponential map
zbMATH Keywords: Finsler manifold
zbMATH Keywords: cut locus
zbMATH Keywords: Azimuthal equidistant projection
Wikidata QID: Q115497258
MaRDI profile type: Publication
full work available at URL: pjm.2020.308.73
OpenAlex ID: W3107954817
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DOI: 10.2140/PJM.2020.308.73
description: scientific article; zbMATH DE number 7291147