Indefinite Finsler Spaces and Timelike Spaces

In this paper we investigate indefinite Finsler spaces in which the metric tensor has signature n — 2. These spaces are a generalization of Lorentz manifolds. Locally a partial ordering may be defined such that the reverse triangle inequality holds for this partial ordering. Consequently, the spaces we study may be made into what Busemann [ 3 ] terms locally timelike spaces. Furthermore, sufficient conditions are obtained for an indefinite Finsler space to be a doubly timelike surface (see [ 2; 4 ]). In particular, all two-dimensional pseudo-Riemannian spaces are shown to be doubly timelike surfaces.