Locus of the centers of Meusnier spheres in Euclidean 3-space
Abstract
In this study, we investigate the locus of the centers of the Meusnier spheres. Just as focal curve is the locus of the centers of the osculating spheres, we investigate the geometrical interpretation on the locus of the centers of the Meusnier spheres. We proved that if the curve is a principal line, the locus of the centers of the Meusnier spheres of the curve is an evolute curve. Then, we give the relations between this evolute curve and the focal curve. Also, we give some relations between helices, slant helices and the locus of the centers of the Meusnier spheres of the curve.
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