Finsler geometries from topological electromagnetism

Billiards in Finsler and Minkowski geometries

We begin the study of billiard dynamics in Finsler geometry. We deduce the Finsler billiard reflection law from the “least action principle”, and extend the basic properties of Riemannian and Euclidean billiards to the Finsler and Minkowski settings, respectively. We prove that the Finsler billiard map is a symplectomorphism, and compute the mean free path of the Finsler billiard ball. For the ...

A Class of Anisotropic (finsler-) Space-time Geometries

A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions (null, spaceor timelike). The metrics are classified according to their group of isometries. These turn out to be isomorphic to subgroups of the Poincaré (Lore...

Finsler and Lagrange Geometries in Einstein and String Gravity

We review the current status of Finsler–Lagrange geometry and generalizations. The goal is to aid non–experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Finsler and Kähler g...

Topological Relationships between Map Geometries

The importance of topological relationships between spatial objects is recognized in many disciplines. In the field of spatial databases, topological relationships have played an important role, providing mechanisms for spatial constraint specification and spatial indexing techniques. The use of spatial data in a map form has become popular, resulting in spatial data models such as topologies o...

Topological Dynamics of Nonstrictly Convex Hilbert Geometries