Geodesics on strong Kropina manifolds
We study the behavior of the geodesics of strong Kropina spaces. The global and local aspects of geodesics theory are discussed. Our theory is illustrated with several examples.
math.DG↗
arXiv subjects
Ryozo Yoshikawa
Publications and source records attributed to Ryozo Yoshikawa.
Some remarks on the geometry of Kropina spaces
Using the navigation data (h,W) of a Kropina space, we characterize weakly-Berwald Kropina spaces and Berwald Kropina spaces by means of the Killing vector field W and the parallel vector field W, respectively. Moreover, the local 1-parameter group of Finslerian local isometries of the Kropina space coincides with the local 1-parameter group Riemannian of local isometries on (M, h).
math.DG↗
Kropina metrics and Zermelo navigation on Riemannian manifolds
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.
math.DG↗