Shape Operator via Darboux Frame Curvatures and Its Applications

Authors : Bahar Uyar DÜLDÜL, Mustfa DÜLDÜL

Pages : 182-187

Doi:10.36890/iejg.628075

View : 50 | Download : 7

Publication Date : 2019-10-03

Article Type : Research Paper

Abstract :We present the shape operator’s matrix of a surface along a surface curve. By using the obtained matrix, we give a short proof of the Beltrami-Enneper theorem. Also, we give a new method for  determining the well-known geodesic curves of a plane, a sphere and a circular cylinder by using  the relation between the ordinary curvatures of the geodesic and the curvatures of the surface.
Keywords : Shape operator, Darboux frame, curvature, geodesic curve

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