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Acta Mathematica Vietnamica

THE BERTRAND OFFSETS OF RULED SURFACES IN R13

icon-email E. KASAP, N. KURUOGLU

Abstract

The problem of finding a curve whose principal normals are also the principal normals of another curve was apparently first proposed by Saint-Venant but solved by J. Bertrand. Such curves were referred to as ‘Bertrand offsets’. In this paper, a generalization of the theory of Bertrand curves is presented for ruled surfaces in Minkowski space R13. Using lines instead of points, two ruled surfaces which are offset in the sense of Bertrand are defined. The obtained results are illustrated by computer-aided examples.