• Korean Journal of Mathematics
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• v.27 no.4
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• pp.1149-1157
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• 2019

We prove the Frenet type formulae for smooth one-parameter family of 2-planes or 3-planes in the Lorentz-Minkowski space 𝕃⁶. We consider two cases separately: the planes are spacelike or the planes are timelike.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.475-492
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• 2014

In this study, we have investigated the possibility of whether any spacelike Frenet plane of a given space curve in Minkowski 3-space $\mathbb{E}_1^3$ also is any spacelike Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.113-129
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• 2014

In this study, we have investigated the possibility of whether any Frenet plane of a given space curve in a 3-dimensional Euclidean space $\mathbb{E}_3$ also is any Frenet plane of another space curve in the same space. We have obtained some characterizations of a given space curve by considering nine possible case.