Minimal entropy rigidity for Finsler manifolds of negative
Abstract. We define a normalized entropy functional for compact Finsler manifolds of negative flag curvature. Using the method of Besson, Courtois, and Gallot, we show that among all such manifolds which are homotopy equivalent to a compact, Riemannian, locally symmetric manifold of negative curvature, the entropy functional is minimized precisely on the locally symmetric manifold.
Projectively flat Finsler 2-spheres of constant curvature
In this interesting paper, the author extends the work of Funk and classifies the (not-necessarily symmetric) Finsler structures on the 2-sphere that have constant Finsler-Gauss curvature and whose geodesics are great circles. The paper is mostly self-contained and includes a very clear account of Berwald's work on the projective equivalence of Finsler surfaces.
This paper appeared in Selecta Math. New. Ser. 3, No.2 (1997), 161-203. Fortunately, an electronic version can also be found on the Web.
Finsler surfaces with prescribed curvature conditions
In this paper Bryant proposes an interesting and useful generalization of (non reversible) Finsler surfaces in terms of Cartan's structure equations. He also studies the spaces of geodesics of Finsler surfaces with constant curvature and constructs some examples of non reversible Finsler two-spheres of curvature one.
Finsler surfaces with prescribed curvature conditions is available electronically as a dvi file.
Some remarks on Finsler manifolds with constant flag curvature
In this paper Bryant studies the space of geodesics of a Finsler metric of constant curvature on the n-sphere. Two of his main results are that the space of geodesics of such a metric has a natural Kahler structure and that there is a description of Finsler metrics of constant curvature on the 2-sphere in terms of a Riemannian metric and a 1-form on its space of geodesics.
This paper can be downloaded from the arXiv.