Finsler metrics with properties of the Kobayashi metric on convex domains (Q1199344)

The paper discusses the structure of complex Finsler manifolds when the Finsler metric has the property of the Kobayashi metric on a convex domain: real geodesics locally extend to complex curves (extremal disks). This property of the Finsler metric induces a complex foliation of the cotangent space closely related to geodesics and each geodesic of the metric has a unique extension to a maximal totally geodesic complex curve with the properties of extremal disks. Furthermore a theorem of Faran is recovered [\textit{J. J. Faran}, J. Differ. Geom. 31, No. 3, 601-625 (1990; Zbl 0709.53020)].