On Hybrid Curves

In this paper, we first define the vector product in a special analog Minkowski Geometry (R^3,) which is identified with the space of spatial hybrids. Next, we derive the Frenet-Serret frame formulae for a three dimensional non-parabolic curve by using the spatial hybrids and the vector product. How...

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Published inJournal of Engineering Technology and Applied Sciences Vol. 8; no. 3; pp. 119 - 130
Main Author AKBIYIK, Mücahit
Format Journal Article
LanguageEnglish
Published 31.12.2023
Online AccessGet full text
ISSN2548-0391
2548-0391
DOI10.30931/jetas.1338660

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Abstract In this paper, we first define the vector product in a special analog Minkowski Geometry (R^3,) which is identified with the space of spatial hybrids. Next, we derive the Frenet-Serret frame formulae for a three dimensional non-parabolic curve by using the spatial hybrids and the vector product. However, we present the Frenet-Serret frame formulae of a non-lightlike hybrid curve in R^4 and an illustrative example for all theorems of the paper with MATLAB 2016a codes.
AbstractList In this paper, we first define the vector product in a special analog Minkowski Geometry (R^3,) which is identified with the space of spatial hybrids. Next, we derive the Frenet-Serret frame formulae for a three dimensional non-parabolic curve by using the spatial hybrids and the vector product. However, we present the Frenet-Serret frame formulae of a non-lightlike hybrid curve in R^4 and an illustrative example for all theorems of the paper with MATLAB 2016a codes.
Author AKBIYIK, Mücahit
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Cites_doi 10.3390/axioms10030213
10.1016/j.chaos.2019.109449
10.1007/s10711-012-9733-1
10.1002/mma.6580
10.1016/S0096-3003(03)00783-5
10.2298/FIL1904037D
10.7151/dmgaa.1287
10.1007/s00006-018-0833-3
10.1007/s00006-018-0919-y
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