On 1-form finsler spaces

By definition, the metric of N-dimensional 1-form Finsler space is constructed proceeding from, in general arbitrary, Minkowskian metric by means of an N-dimensional reference frame, i.e., in other words, by means of N independent linear 1-forms. In the present paper, the attention is drawn to the fact that a preferred osculating Riemannian space with simple but interesting properties exists for a 1-form Finsler space. Then, some significant simplifications are emphasized which are imposed by the conditions C_i=0 in a 1-form Finsler space. The T- condition and S3-likeness give rise to additional simplifications. Since the 1-form Berwald- Moór's metric exhibits all three properties mentioned above, a fairly simple expression for the curvature scalar H = H^ij_ij of this metric may be calculated. In conclusion, the attention is drawn to the fact that the assumption of a 1-form structure of the space-time is certainly expedient in obtaining a deeper insight into the Finslerian relativity.