Kropina metrics and Zermelo navigation on Riemannian manifolds

Ryozo Yoshikawa; Sorin V. Sabau

Kropina metrics and Zermelo navigation on Riemannian manifolds

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arxiv 1209.0340 v1 pith:5H54FINP submitted 2012-09-03 math.DG

Ryozo Yoshikawa , Sorin V. Sabau This is my paper · ORCID

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keywords kropinametricsnavigationzermelocharacterizeconstantcurvaturedefined

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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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The causal structure of black holes, including horizons and interiors, can be encoded in wind-Finsler metrics whose shifted indicatrices track null geodesics.

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