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

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

1
C.B.Ü. Fen Edebiyat Fakültesi Matematik Bölümü, 45040 MANİSA, Turkey
2
E.Ü. Fen Fakültesi Matematik Bölümü, 35000 Bornova İZMİR, Turkey
*
Author to whom correspondence should be addressed.
Published: 1 December 1996
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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.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Kılıç, O.; Çalışkan, A. The Frenet and Darboux Instantaneous Rotation for Curves on Space-Like Surface. Math. Comput. Appl. 1996, 1, 77-86.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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