Zermelo deformation of Finsler metrics by Killing vector fields

We show how geodesics, Jacobi vector fields and flag curvature of a Finsler metric behave under Zermelo deformation with respect to a Killing vector field. We also show that Zermelo deformation with respect to a Killing vector field of a locally symmetric Finsler metric is also locally symmetric.

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Bibliographic Details
Published inarXiv.org
Main Authors Foulon, Patrick, Matveev, Vladimir S
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.10.2017
Subjects
Economic models
Fields (mathematics)
Geodesy
Mathematics - Differential Geometry
Mathematics - Dynamical Systems
Production planning
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Summary:We show how geodesics, Jacobi vector fields and flag curvature of a Finsler metric behave under Zermelo deformation with respect to a Killing vector field. We also show that Zermelo deformation with respect to a Killing vector field of a locally symmetric Finsler metric is also locally symmetric.
ISSN:2331-8422
DOI:10.48550/arxiv.1710.01281