After recalling the structure equations of Finsler structures on surfaces, I define a notion of ‘generalized Finsler structure’ as a way of micro-localizing the problem of describing Finsler structures subject to curvature conditions. I then recall the basic notions of path geometry on a surface and define a notion of ‘generalized path geometry’ analogous to that of ‘generalized Finsler structu...

It is reasonably well-known that birefringent crystal optics can to some extent be described by the use of pseudo–Finslerian spacetimes (an extension of the natural pseudo-Riemannian Minkowski spacetime one encounters in mono-refringent situations). What is less commonly appreciated is that there are two separate and quite disjoint pseudo–Finsler structures for the two photon polarizations, and...

Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann model is proposed. It is showed that the accelerated expanding universe is guaranteed by a constrained RandersFinsler structure without invoking dark energy. The geodesic in Randers-Finsler space is studied. The additional term in the geodesic equation acts as repulsive forc...

In this paper, nonholonomic gerbes will be naturally derived for manifolds and vector bundle spaces provided with nonintegrable distributions (in brief, nonholonomic spaces). An important example of such gerbes is related to distributions defining nonlinear connection (N–connection) structures. They geometrically unify and develop the concepts of Riemann–Cartan manifolds and Lagrange–Finsler sp...

G. W. Gibbons, Joaquim Gomis, and C. N. Pope DAMTP, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA, United Kingdom Departament ECM, Facultat de Fı́sica, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain George P. and Cynthia W. Mitchell Institute for Fundamental Physics, Texas A&M University, College Station, Texas 77843-4242, USA (Rece...

This article is an exposition of four loosely related remarks on the geometry of Finsler manifolds with constant positive flag curvature. The first remark is that there is a canonical Kähler structure on the space of geodesics of such a manifold. The second remark is that there is a natural way to construct a (not necessarily complete) Finsler n-manifold of constant positive flag curvature out ...