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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.
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참고문헌 (17)
참고문헌 신청
Ahmad T. Ali / 2011 / SLANT HELICES IN MINKOWSKI SPACE <수식> / 대한수학회지 48(1):159~167
A. T. Ali / 2010 / Position vector of a timelike slant helix in Minkowski 3-space / Journal of Mathematical Analysis and Applications 365:559~569
J. K. Beem / 1981 / Global Lorentzian Geometry / Marcel Dekker
B. Y. Chen / 2003 / When does the position vector of a space curve always lie in its Rectifying plane? / American Mathematical Monthly 110:147~152
J. H. Choi / 2012 / Associated curves of a Frenet curve and their applica- tions / Applied Mathematics and Computation 218:9116~912
A. T. Ali / 2010 / Position vector of a timelike slant helix in Minkowski 3-space / Journal of Mathematical Analysis and Applications 365:559~569
J. K. Beem / 1981 / Global Lorentzian Geometry / Marcel Dekker
B. Y. Chen / 2003 / When does the position vector of a space curve always lie in its Rectifying plane? / American Mathematical Monthly 110:147~152
J. H. Choi / 2012 / Associated curves of a Frenet curve and their applica- tions / Applied Mathematics and Computation 218:9116~912
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