The navigation problems on a class of conic Finsler manifolds
type: Item
instance of: scholarly article
title: The navigation problems on a class of conic Finsler manifolds
zbMATH Open document ID: 1477.53031
author: Qiuhong Qu
author: Suiyun Xu
author: Xinyue Cheng
published in: Differential Geometry and its Applications
publication date: 2021-02-24T00:00:00Z
review text: Emerging from the deep understanding of the essential relationships between the Zermelo navigation problems and the indicatrix geometry on Finsler manifolds, the authors study navigation problems on conic Kropina manifolds. For a conic Kropina metric \(F(x,y)\) and a vector field \(V\) with \(F(x,-V_x)\le 1\) on an \(n\)-dimensional manifold \(M\), let \({\tilde F}={\tilde F}(x,y)\) be the solution of the navigation problem with navigation data \((F,V)\). It is proved that \({\tilde F}\) must be either a Randers metric or a Kropina metric. Then, several relationships are established between certain curvature properties of \(F\) and the corresponding properties of \({\tilde F}\), when \(V\) is a conformal vector field on \((M,F)\), which involve \(S\)-curvature, flag curvature and Ricci curvature.
reviewed by: Vladimir Balan
Mathematics Subject Classification ID: 53B40
Mathematics Subject Classification ID: 53C60
zbMATH DE Number: 7315197
zbMATH Keywords: Zermelo navigation problem
zbMATH Keywords: Kropina metric
zbMATH Keywords: Randers metric
zbMATH Keywords: S-curvature
zbMATH Keywords: flag curvature
zbMATH Keywords: Ricci curvature
MaRDI profile type: Publication
full work available at URL: j.difgeo.2020.101709
OpenAlex ID: W3106763602
Wikidata QID: Q115354653
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DOI: 10.1016/J.DIFGEO.2020.101709
description: scientific article; zbMATH DE number 7315197