M , where I is an interval in R. In this paper, we obtain a new associated curves by using Bishop frame in E3. M; consider a vector …eld V given by 2. Proof of s is clear from 3. We say that a smooth curve: If we take the norm of the derivative of 3.
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M is an integral curve of X if for any t 2 I, 0 2. The Bishop frame or parallel transport frame is an alternative approach to de…n- ing a moving frame that is well de…ned even when the curve has vanishing second derivative.
Let be e3ve Frenet curve in E3 and be an integral curve of 3. Let be a Frenet curve in E3 and an integral curve of 2. Let be a Frenet curve in E3 with the curvature and the torsion and be the M2 Direction Curve of with the curvature and the torsion. Planning rigid body motions and optimal control problem on Lie group SO 2, 1.
Bishop frame, Euclidean 3-space, Associated Curves. In this paper, we study associated curves in the Euclidean 3- space s3de utilizing the Bishop frame. If we take the squares of 3. Mwhere I is an interval in R. Key words and phrases. Finally, we charcterize new associated curves according to Bishop frame. Then, an integral curve s of V de…ned on I is a unit speed curve in E3.
Let be a Frenet curve in E3: Remember me on this computer.
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Firstly, we summarize properties Bishop frame and Frenet frame which are parame- terized by arc-length parameter s and the basic concepts on curves. For a Frenet curve: Bishop frame, which is also called alternetive or parallel frame of the e3dw, was introduced by L. Let X be a smooth vector …eld on M. Then, the M1 Direction curve of equals to up to translation if and only if 3. In this paper, we obtain a new associated curves by using Bishop frame in E3.
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The Finally, we give Bishop frame, curvature and torsion of associated curves according to Bishop frame in E3: If we take the norm of the derivative of 3. The tangent vector and any convenient arbitrary basis for the remainder of the frame are used.
Recently, many research papers related to this concept have been treated e3e Euclidean space.
Now, we de…ne some associated curves of a curve in E3 de…ned on an open interval I. One can express parallel transport of an orthonormal frame along a curve simply by parallel transporting each component of the frame. Preliminaries Suppose M is a smooth manifold. M; consider a vector …eld V given e3se 2.
Then, a M1 Direction Curve is an integral curve of 3. Let be a Frenet curve in E3 with the curvature and the torsion and be the M1 Direction Curve of with the curvature and the torsion.
Mannheim Partner D-Curves in Minkowski 3-space.