On Δ‐principal directions of a congruence of curves in a F INSLER hypersurface

In the existing literature of F INSLER spaces, it has been stressed [E LIOPOULOS 1959, R UND 1956] that the process of Δ‐differentiation leads to the use of D UPIN 's indicatrix in finding out the principal directions at a point of a hypersurface which are indeterminate. The process of Δ‐differentiation [4, 7] requires the use of the osculating D UPIN 's indicatrix corresponding to a line‐element of F INSLER hypersurface which leads to the linear eigen value problem and thereby helps in determining the principal directions of a congruence of curves. This fact increases the scope of the theory of F INSLER spaces to a considerable extent. In this paper, therefore, an attempt has been made to find the Δ‐principal directions, generalized E ULER 's theorem, minimal congruences, Δ‐geodesic principal directions and Δ‐absolute curvature of the congruence with respect of a curve of F n −1 .