Kropina metrics and Zermelo navigation on Riemannian manifolds

2012/09/03 by Ryozo Yoshikawa, Yoshikawa, Ryozo, Sorin V. Sabau +1 · 3 citations
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1209.0340

arxiv created 2012/09/03 · arxiv updated 2012/09/04

Abstract

The present paper studies globally defined Kropina metrics as solutions of the Zermelo's navigation problem. Moreover, we characterize the Kropina metrics of constant flag curvature showing that up to local isometry, there are only two model spaces of them: the Euclidean space and the odd-dimensional spheres.

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