Abstract
In this paper, we investigate special Smarandache curves accord- ing to Bishop frame in Euclidean 3-space and we give some differential geomet- ric properties of Smarandache curves. Also we find the centers of the osculating spheres and curvature spheres of Smarandache curves. The Bishop frame or parallel transport frame is an alternative approach to defin- ing a moving frame that is well defined even when the curve has vanishing second derivative. We can parallel transport an orthonormal frame along a curve simply by parallel transporting each component of the frame. The parallel transport frame is based on the observation that, while T(s) for a given curve model is unique, we may choose any convenient arbitrary basis (N1(s),N2(s)) for the remainder of the frame, so long as it is in the normal plane perpendicular to T(s) at each point. If the derivatives of (N1(s),N2(s)) depend only on T(s) and not each other we
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