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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Previous articles were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence, and they are hosted by MDPI on mdpi.com as a courtesy and upon agreement with Association for Scientific Research (ASR).
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Article

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

by
Osman Kılıç
1,* and
Ali Çalışkan
2
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.
Math. Comput. Appl. 1996, 1(2), 77-86; https://doi.org/10.3390/mca1020077
Published: 1 December 1996
Versions Notes

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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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. https://doi.org/10.3390/mca1020077

AMA Style

Kılıç O, Çalışkan A. The Frenet and Darboux Instantaneous Rotation for Curves on Space-Like Surface. Mathematical and Computational Applications. 1996; 1(2):77-86. https://doi.org/10.3390/mca1020077

Chicago/Turabian Style

Kılıç, Osman, and Ali Çalışkan. 1996. "The Frenet and Darboux Instantaneous Rotation for Curves on Space-Like Surface" Mathematical and Computational Applications 1, no. 2: 77-86. https://doi.org/10.3390/mca1020077

APA Style

Kılıç, O., & Çalışkan, A. (1996). The Frenet and Darboux Instantaneous Rotation for Curves on Space-Like Surface. Mathematical and Computational Applications, 1(2), 77-86. https://doi.org/10.3390/mca1020077

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