Zermelo navigation in pseudoFinsler metrics
Abstract
We generalize the notion of Zermelo navigation to arbitrary pseudoFinsler metrics possibly defined in conic subsets. The translation of a pseudoFinsler metric $F$ is a new pseudoFinsler metric whose indicatrix is the translation of the indicatrix of $F$ by a vector field $W$ at each point, where $W$ is an arbitrary vector field. Then we show that the Matsumoto tensor of a pseudoFinsler metric is equal to zero if and only if it is the translation of a semiRiemannian metric, and when $W$ is homothetic, the flag curvature of the translation coincides with the one of the original one up to the addition of a nonpositive constant. In this case, we also give a description of the geodesic flow of the translation.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.0465
 Bibcode:
 2014arXiv1412.0465J
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 23 pages