• The Pure and Applied Mathematics
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• v.12 no.3 s.29
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• pp.211-221
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• 2005

The purpose of this paper is to study the geometry of null curves in a Lorentzian manifold (M, g). We show that it is possible to construct new type of Frenet equations of null curves in M, supported by two examples.

• The Pure and Applied Mathematics
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• v.10 no.2
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• pp.71-102
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• 2003

The purpose of this paper is to study the geometry of null curves in a 6-dimensional semi-Riemannian manifold $M_q$ of index q, since the general n-dimensional cases are too complicated. We show that it is possible to construct three types of Frenet equations of null curves in $M_q$, supported by one example. We find each types of Frenet equations invariant under any causal change. And we discuss some properties of null curves in $M_q$.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.231-253
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• 2007

The purpose of this paper is to study the geometry of null curves in a semi-Riemannian manifold (M, g) of index 2. We show that it is possible to construct new Frenet equations of two types of null curves in M.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.513-541
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• 2023

In this paper, we calculate Frenet frames, Frenet derivative formulas, curvatures, arc lengths, geodesic curvatures according to the Lorentzian 3-space ℝ³₁, Lorentzian sphere 𝕊²₁ and hyperbolic sphere ℍ²₀ of the spherical indicatrix curves of the spacelike Salkowski curve with the timelike principal normal in ℝ³₁ and draw the graphs of these indicatrix curves on the spheres.

• The Pure and Applied Mathematics
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• v.15 no.3
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• pp.209-215
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• 2008

The purpose of this paper is to study the geometry of null Bertrand curves in a Lorentz manifold.

• The Pure and Applied Mathematics
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• v.10 no.1
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• pp.13-23
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• 2003

The purpose of this paper is to prove the fundamental existence and uniqueness theorems for lightlike curves in a 6-dimensional semi-Euclidean space Rq of index q, since the general n-dimensional cases are too complicated.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.31-46
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• 2009

In this paper we study the geometry of Einstein half light like submanifolds M of a Lorentz manifold ($\bar{M}$(c), $\bar{g}$) of constant curvature c, equipped with an integrable screen distribution on M such that the induced connection ${\nabla}$ is a metric connection and the operator $A_u$ is a screen shape operator.

• Journal of the Korea Computer Graphics Society
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• v.16 no.4
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• pp.41-50
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• 2010

We present a new technique for multilevel editing of hierarchical B-spline curves. At each level, control points of a displacement function are expressed in the rotation minimizing frames (RMFs) [1] which are computed on nodal points of the curve at previous level. When the curve is edited at previous level, the corresponding RMFs are updated and the control points of the displacement function at current level are applied to the new RMFs, which maintains the relative details of the curve at current level to those of previous level. We demonstrate the effectiveness and robustness of the proposed technique using several experimental results.