Projectively flat Finsler 2-spheres of constant curvature (Q1366757)

The author develops a generalization of Finsler structures based on a Cartan method of coframing on a 3-manifold. This produces a corresponding path geometry, the geometry of a surface endowed with a 2-parameter family of curves. This new geometry is applied to 2-spheres of constant Finsler-Gauss curvature \(K\) with projectively flat geodesic path geometry. A family of structures on the sphere with \(K\) identically equal to 1 is identified.