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. Introduction2. Wind Finslerian structures3. Fermat structures for SSTK\xspace splittings4. The case of causal $K$: Randers-Kropina metrics5. The case of arbitrary $K$: General wind Riemannian structures6. Applications to wind Riemannian structures and navigation7. Fermat's principle and generalized Zermelo navigation problem8. Further applications9. Conclusions and further developmentsAppendix: List of some symbols and conventions