Shape Operator via Darboux Frame Curvatures and Its Applications

Year 2019, Volume: 12 Issue: 2, 182 - 187, 03.10.2019

Bahar Uyar Düldül , Mustfa Düldül

https://doi.org/10.36890/iejg.628075

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

References

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