Abstract
We investigate differential geometry of Bertrand curves in 3-dimensional space form from a viewpoint of curves on surfaces. We define a special kind of surface, named geodesic surface, generated by geodesics in 3-dimensional space form. This kind of surface is nothing else, but a generalization of ruled surface in 3-dimensional Euclidean space. As results, we show that the Bertrand curve is related to the mean curvature of principal normal geodesic surface.
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