Resumen de Kähler and para-Kähler structures associated with Finsler spaces of non-zero constant flag curvature
It was shown by R.,L. Bryant (Houston J. Math. 28 (2002) 221-262) that there is a canonical Kähler structure on the space of geodesics of a Finsler manifold whose flag curvature is constant and positive. A different construction is proposed in the present paper, leading instead to a Kähler structure on the slit tangent bundle of the Finsler space; it is based on the identification of an appropriate complex structure. The construction is easily adapted to apply to a Finsler space with constant negative flag curvature, when it gives a para-Kähler rather than a Kähler structure; the properties of this para-Kähler structure are explored.
