• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.665-673
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• 2011

In this paper, we derive a set of the partial differential equations that characterize an inelastic flow of a curve in a 3-dimensional Galilean space. Also, we give necessary and sufficient condition for an inelastic flow.

• Communications of the Korean Mathematical Society
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• v.36 no.3
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• pp.609-622
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• 2021

In the Galilean space G₃, we study a special kind of tube surfaces, called tube-like surfaces. They are defined by sweeping a space curve along another central space curve. In this setting, we investigate some equations in terms of Gaussian and mean curvatures, showing some relevant theorems. Our theoretical results are illustrated with some plotted examples.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.769-780
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• 2020

In this paper, Fermi-Walker derivative for inextensible flows of curves are researched in 3-dimensional Galilean space G3. Firstly using Frenet and Darboux frame with the help of Fermi-Walker derivative a new approach for these flows are expressed, then some results are obtained for these flows to be Fermi-Walker transported in G3.

• Honam Mathematical Journal
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• v.37 no.2
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• pp.253-264
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• 2015

In the present paper, we consider a position vector of an arbitrary curve in the three-dimensional Galilean space $G_3$. Furthermore, we give some conditions on the curvatures of this arbitrary curve to study special curves and their Smarandache curves. Finally, in the light of this study, some related examples of these curves are provided and plotted.

• Honam Mathematical Journal
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• v.40 no.2
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• pp.251-264
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• 2018

In the present study, we consider the curves in Galilean 4-space ${\mathbb{G}}_4$. We find out the involute curves of order k (k = 1, 2, 3) of a given curve. We get the relationships between the Frenet apparatus of a given curve and its involute curves of order k.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.361-373
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• 2020

In this paper, we define admissible canal surfaces with isotropic radius vectors in pseudo-Galilean 3-spaces and we obtaine their position vectors. We also attain some important results by considering their Gauss and mean curvatures.

• Kyungpook Mathematical Journal
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• v.57 no.2
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• pp.319-326
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• 2017

In this paper, we defined the admissible canal surfaces with isotropic radious vector in Galilean 3-spaces an we obtained their position vectors. Also we gave some important results by using their Gauss and mean curvatures.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.167-177
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• 2022

In this manuscript, we handle a tubular surface whose Gauss map G satisfies the equality L₁G = f(G + C) for the Cheng-Yau operator L₁ in Galilean 3-space 𝔾₃. We give an example of a tubular surface having L₁-harmonic Gauss map. Moreover, we obtain a complete classification of tubular surface having L₁-pointwise 1-type Gauss map of the first kind in 𝔾₃ and we give some visualizations of this type surface.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.497-507
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• 2022

In this study, we define tubular surfaces in Pseudo Galilean 3-space as type-1 or type-2. Using the X(s, t) position vectors of the surfaces and G(s, t) Gaussian transformations, we obtain equations for the two types of tubular surfaces that satisfy the conditions ∆X(s, t) = 0, ∆X(s, t) = AX(s, t), ∆X(s, t) = λX(s, t), ∆X(s, t) = ∆G(s, t), ∆G(s, t) = 0, ∆G(s, t) = AG(s, t) and ∆G(s, t) = λG(s, t).

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.585-597
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• 2020

In this study, we classify surfaces of revolution of Type 1 in the three dimensional Galilean space 𝔾₃ in terms of the position vector field, Gauss map, and Laplacian operator of the first and the second fundamental forms on the surface. Furthermore, we give a classification of surfaces of revolution of Type 1 generated by a non-isotropic curve satisfying the pointwise 1-type Gauss map equation.