On The Motion Of The Frenet Trihedron of a Space Curve

Abstract

in 1963 Hans Vogler in his paper called “Dje auf einer Torse verlaufenden Linien konstanten Gratabstandes als duale Seitenstücke zu den pseudorektifizieren den Torsen einer Raumkurve” has studied the geometrical varieties formed by the elements of the moving FRENET trihedron along the curve traced on a developable at a constant distance froih its edge of regression. The developable itself is the dual correspondiug of the pseudö-rectifying developable of a space curve. In this paper we have studied the geometrical varieties of the elements of the ıçoving Frenet trihedron along the parametric curves of the skew surface generated by a straight line fastened, in the rectifying plane, to the moving Frenet trihedron of a space curve. The parametric curves vzhich are taken into consideration have given more general results than the curves at a constant distance fcom the edge of regression. Thus we were able to deduce the same results of Hans Vogler as special cases of the problem.

Keywords

• The Motion
• Frenet Trihedron
• Space Curve

References

1. Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi