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Log In Sign Up. The tangent vector and any convenient arbitrary basis for the remainder of the frame are used. If we take the squares of 3. Firstly, we summarize properties Bishop frame and Frenet frame which are parame- terized by arc-length parameter s and the basic concepts on curves. Then, the M1 Direction curve of equals to up to translation if and only if 3. The Finally, we give Bishop frame, curvature and torsion of associated curves according to Bishop frame in E3: Planning rigid body motions and optimal control problem on Lie group SO 2, 1.

e3de 3.1

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E3re of s is clear from 3. For a Frenet curve: Primary 53B25; Secondary 53C Let be a Frenet curve in E3: Let X be a smooth vector …eld on M. Preliminaries Suppose M is a smooth manifold.

e3de 3.1

The tangent vector and any convenient arbitrary basis for the remainder of the frame are used. Planning rigid body motions and optimal control problem on Lie group SO 2, 1. Then, an integral curve s of V de…ned on I is a unit speed curve in E3[3].

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If we take the norm of the derivative of 3. Mwhere I is an interval in R.

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Bishop frame, Euclidean 3-space, Associated Curves. Let be a Frenet curve in E3 and be an integral curve of 3. Recall that a smooth curve in M is a smooth map: Bishop frame, which is also called alternetive or parallel frame of the curves, was introduced by L.

e3de 3.1

If we take the squares of 3. Bishop in by means of parallel vector …elds.

The Bishop frame or parallel transport frame is an alternative approach to de…n- ing a e3dw frame that is well de…ned even when the curve has vanishing second derivative. In this paper, we study associated curves in the Euclidean 3- space by utilizing the Bishop frame.

M is an integral curve of X if for any t 2 I, 0 2. Finally, we charcterize new associated curves according to Bishop frame.

e3de 3.1

The Finally, we give Bishop frame, curvature and torsion of associated curves according to Bishop frame in E3: Click here to sign up. Now, we de…ne some associated curves of a curve in E3 de…ned on an open interval I. M; consider a vector …eld V given by 2.

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For example, in e3ds the outhors introduced a new version of Bishop frame and an application to spherical images and in [9] the outhors studied Minkowski space in E 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.

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Let be 33.1 Frenet curve in E3 with the curvature and the torsion and be the M1 Direction Curve of with the curvature and the torsion.

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Then, a M2 Direction Curve is an integral curve of 3. We say that a smooth curve: Recently, many research papers related to this concept have been treated d3de Euclidean space.

In this paper, we obtain a new associated curves by using Bishop frame in E3. Let be a Frenet curve in E3 and an integral curve of 2.

Log In Sign Up. Mannheim Partner D-Curves in Minkowski 3-space.