• Honam Mathematical Journal
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• v.40 no.2
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• pp.305-314
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• 2018

In this paper, we investigate the notions of helix and slant helices in the lightlike cone. Using the asymptotic orthonormal frame we present some characterizations of helices and slant helices.

• Kyungpook Mathematical Journal
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• v.52 no.1
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• pp.49-59
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• 2012

In this article, using the example of C. Camci([7]) we reconfirm necessary sufficient condition for a slant curve. Next, we find some necessary and sufficient conditions for a slant curve in a Sasakian 3-manifold to have: (i) a $C$-parallel mean curvature vector field; (ii) a $C$-proper mean curvature vector field (in the normal bundle).

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1485-1500
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• 2021

A curve is rectifying if it lies on a moving hyperplane orthogonal to its curvature vector. In this work, we extend the main result of [Chen 2017, Tamkang J. Math. 48, 209] to any space dimension: we prove that rectifying curves are geodesics on hypercones. We later use this association to characterize rectifying curves that are also slant helices in three-dimensional space as geodesics of circular cones. In addition, we consider curves that lie on a moving hyperplane normal to (i) one of the normal vector fields of the Frenet frame and to (ii) a rotation minimizing vector field along the curve. The former class is characterized in terms of the constancy of a certain vector field normal to the curve, while the latter contains spherical and plane curves. Finally, we establish a formal mapping between rectifying curves in an (m + 2)-dimensional space and spherical curves in an (m + 1)-dimensional space.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.233-251
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• 2014

In this paper, position vector of a spacelike slant helix with respect to standard frame are deduced in Minkowski space $E^3_1$. Some new characterizations of a spacelike slant helices are presented. Also, a vector differential equation of third order is constructed to determine position vector of an arbitrary spacelike curve. In terms of solution, we determine the parametric representation of the spacelike slant helices from the intrinsic equations. Thereafter, we apply this method to find the parametric representation of some special spacelike slant helices such as: Salkowski and anti-Salkowski curves.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1309-1320
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• 2018

In this paper, we show that proper biharmonic spacelike curve ${\gamma}$ in Lorentzian Heisenberg space (${\mathbb{H}}_3$, g) is pseudo-helix with ${\kappa}^2-{\tau}^2=-1+4{\eta}(B)^2$. Moreover, ${\gamma}$ has the spacelike normal vector field and is a slant curve. Finally, we find the parametric equations of them.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.225-236
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• 2021

In this paper, we determine position vector of a line of curvature of a regular surface which is relatively normal-slant helix, with respect to Darboux frame. Then, a vector differential equation is established by means Darboux formulas, in the case of the geodesic torsion is vanishes. In terms of solution, we determine the parametric representation of a line of curvature which is relatively normal-slant helix, with respect to standard frame in Euclidean 3-space. Thereafter, we apply this result to find the position vector of a line of curvature which is isophote curve.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.159-167
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• 2011

We consider a curve $\alpha$= $\alpha$(s) in Minkowski 3-space $E_1^3$ and denote by {T, N, B} the Frenet frame of $\alpha$. We say that $\alpha$ is a slant helix if there exists a fixed direction U of $E_1^3$ such that the function is constant. In this work we give characterizations of slant helices in terms of the curvature and torsion of $\alpha$. Finally, we discuss the tangent and binormal indicatrices of slant curves, proving that they are helices in $E_1^3$.

• Proceeding of EDISON Challenge
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• 2015.03a
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• pp.559-562
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• 2015

본 연구에서는 EDISON_CFD를 활용하여 승용차 모델을 단순화한 Ahmed Body의 후미 경사각 Slant angle $0^{\circ}$, $15^{\circ}$, $30^{\circ}$, $45^{\circ}$의 항력계수변화를 확인하였다. 결과 분석을 통해 Ahmed Body 후면의 후류와 항력계수의 변화 경향성이 같다는 것을 확인하였다. 항력계수는 자동차의 연비 및 최고속도 등 동력성능에 큰 영향을 미치므로 최저 항력계수를 찾아보았다. 각각의 경우에 EDISON_simulation 결과 값을 비교해보면 $15^{\circ}{\sim}30^{\circ}$ 사이에서 최저 항력계수를 갖는 것을 확인할 수 있었다. 정확한 값을 찾기 위해 Polynomial Curve Fitting을 사용하여 Slant angle 이 $22.91^{\circ}$일 때 최저항력계수 0.1375를 갖는 것을 확인하였다.

• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.149-158
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• 2013

In this article, we study the Gauss map of generalized slant cylindrical surfaces (GSCS's) in the 3-dimensional Euclidean space $\mathbb{E}^3$. Surfaces of revolution, cylindrical surfaces and tubes along a plane curve are special cases of GSCS's. Our main results state that the only GSCS's with Gauss map G satisfying ${\Delta}G=AG$ for some $3{\times}3$ matrix A are the planes, the spheres and the circular cylinders.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.603-616
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• 2017

In this paper, we give some relations related with a spacelike principal-direction curve and a spacelike binormal-direction curve of a timelike Frenet curve. The Darboux-direction curve and the Darboux-rectifying curve of a timelike Frenet curve in Minkowski 3-space $E^3_1$ are introduced and some characterizations related with these associated curves are given. Later we define the spacelike V-direction curve which is associated with a timelike curve lying on a timelike oriented surface in $E^3_1$ and present some results together with the relationships between the curvatures of this associated curve.