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On Δ-principal directions of a congruence of curves in a FINSLER hypersurface

✍ Scribed by C. M. Prasad

Publisher
John Wiley and Sons
Year
1973
Tongue
English
Weight
443 KB
Volume
57
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In the existing literature of FINSLER spaces, it has been stressed [ELIOPOULOS 1959, RUND 1956] that the process of Δ‐differentiation leads to the use of DUPIN'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 DUPIN's indicatrix corresponding to a line‐element of FINSLER 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 FINSLER spaces to a considerable extent. In this paper, therefore, an attempt has been made to find the Δ‐principal directions, generalized EULER's theorem, minimal congruences, Δ‐geodesic principal directions and Δ‐absolute curvature of the congruence with respect of a curve of F~n −1~.

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