Wind Finslerian Structures: From Zermelo's Navigation to the Causality of Spacetimes

Erasmo Caponio, Politecnico di Bari, Italy, Miguel Angel Javaloyes, Universidad de Murcia, Espinardo, Spain, and Miguel Sanchez, Universidad de Granada, Spain

1. Introduction 2. Wind Finslerian structures 3. Fermat structures for SSTK\xspace splittings 4. The case of causal $K$: Randers-Kropina metrics 5. The case of arbitrary $K$: General wind Riemannian structures 6. Applications to wind Riemannian structures and navigation 7. Fermat's principle and generalized Zermelo navigation problem 8. Further applications 9. Conclusions and further developments Appendix: List of some symbols and conventions