Geometriae Dedicata

, Volume 171, Issue 1, pp 119–148 | Cite as

Kropina metrics and Zermelo navigation on Riemannian manifolds

  • Ryozo Yoshikawa
  • Sorin V. SabauEmail author
Original Paper


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.


Kropina spaces Flag curvature Killing vector fields Riemannian isometries 

Mathematics Subject Classification (2000)

53C60 53C20 



We thank to Professors K. Okubo and H. Shimada for encouraging us in the research of this topic.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Hachiman Technical High SchoolHachimanJapan
  2. 2.Department of MathematicsTokai UniversitySapporoJapan

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