Characteristic properties of the ruled surface with Darboux frame in E^3



In this study, the ruled surface with Darboux frame is defined. Then, the ruled surfacescharacteristic properties which are related to the geodesic curvature, the normal curvature andthe geodesic torsion are investigated. The relation between the Darboux frame and the Frenetframe on the ruled surface is presented. Moreover, some theorems about the pitch and the angleof the pitch which are the integral invariants of the ruled surface with darboux frame are given.


Ruled surface; Darboux frame; integral invariants.

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Hlavaty, V. 1945. Differentielle linien geometrie. Uitg P. Noorfhoff, Groningen.

Hoschek, J. 1973. Integral invarianten Von Regel Flächen. Arch, Math, XXIV.

Müller, H. R. 1978. Verallgemeinerung Einer Formelvon Steiner. Abh. Braunschweig Wiss. Ges.31:107- 113.

Ravani. & Ku, T. S. 1991. Bertrand offsets of ruled surface and developable surface. 23(2): 145-152.

Hacısalihoğlu, H. H. 1994. Diferensiyel geometri. Vol. 2, Ankara Üniversitesi, Fen Fakültesi, Ankara.

Sarıoğlugil, A. & Tutar, A. 2007. On ruled surface in Euclidean space . 3 E Int. J. Contemp. Math. Sci. 2(1): 1-11.

Gray A., Salamon, S. & Abbena E. 2006. Modern differential geometry of curves and surfaces with mathematica, Chapman and Hall/CRC.

Aydemir İ. & Kasap E. 2005. Timelike ruled surface with spacelike rulings 3 R . Kuwait Journal of Science & Engineering. 32(2):13-24.

Darboux, G. 1896. Leçons sur la thèorie gènèrale des sufaces I-II-III-IV. Gauthier- Villars, Paris.

O’Neill, B. 1996. Elementary differential geometry. Academic Press Inc, New York. Pp. 248.


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