The Frenet and Darboux Instantaneous Rotation for Curves on Space-Like Surface

Osman Kılıç; Ali Çalışkan

doi:10.3390/mca1020077

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Article

1 December 1996

The Frenet and Darboux Instantaneous Rotation for Curves on Space-Like Surface

and

C.B.Ü. Fen Edebiyat Fakültesi Matematik Bölümü, 45040 MANİSA, Turkey

E.Ü. Fen Fakültesi Matematik Bölümü, 35000 Bornova İZMİR, Turkey

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Math. Comput. Appl.1996, 1(2), 77-86;https://doi.org/10.3390/mca1020077

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Abstract

In this paper , considering the Darboux instantaneous rotation vector of a solid perpendicular trihedron in the Minkowski 3-space R₁³, the Frenet instantaneous rotation vector was stated for the Frenet trihedron of a space -like space curve (c) with the binormal b being a time-like vector. The Darboux derivative formulas and the Darboux instantaneous rotation vector were found when the curve (c) is on a space -like surface. A fundamental relation, as a base for the geometry of space-like surfaces, was obtained among the Darboux vectors of the parameter curves (c₁) , (c₂) and an arbitrary curve (c) on a space-like surface.

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