Finsler metrics with propierties of the Kobayashi metric on convex domains.
The structure of complex Finsler manifolds is studied when the Finsler metric has the property of the Kobayashi metric on convex domains: (real) geodesics locally extend to complex curves (extremal disks). It is shown that this property of the Finsler metric induces a complex foliation of the cotangent space closely related to geodesics. Each geodesic of the metric is then shown to have a unique extension to a maximal totally geodesic complex curve Σ which has properties of extremal disks. Under...