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2010•International Journal of the Physical SciencesOpen access

Construction of the Frenet-Serret frame of a curve in 4D Galilean space and some applications

Suuml, ha Ylmaz

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Abstract

In this work, first, we construct Frenet-Serret frame of a curve in the Galilean 4-space. As a result of this, we obtain the mentioned curve’s Frenet-Serret equations. Then, we prove that tangent vector of a curve in Galilean 4-space satisfies a vector differential equation of fourth order. Additionally, some characterizations of Galilean spherical curves and an example of the main results are presented.   Key words: Galilean space, Frenet-Serret frame, spherical curves, vector differential equation.

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What this paper is about

In this work, first, we construct Frenet-Serret frame of a curve in the Galilean 4-space. As a result of this, we obtain the mentioned curve’s Frenet-Serret equations. Then, we prove that tangent vector of a curve in Galilean 4-space satisfies a vector differential equation of fourth order. Additionally, some characterizations of Galilean spherical curves and an example of the main results are presented.   Key words: Galilean space, Frenet-Serret frame, spherical curves, vector differential equation.

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OpenAlex reports 11 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this work, first, we construct Frenet-Serret frame of a curve in the Galilean 4-space. As a result of this, we obtain the mentioned curve’s Frenet-Serret equations. Then, we prove that tangent vector of a curve in Galilean 4-space satisfies a vector differential equation of fourth order. Additionally, some characterizations of Galilean spherical curves and an example of the main results are presented.   Key words: Galilean space, Frenet-Serret frame, spherical curves, vector differential equation.

Key concepts: Frenet–Serret formulas, Galilean, Tangent, Space (punctuation), Mathematical analysis, Mathematics, Differential (mechanical device), Physics

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