Surfaces with simple geodesics (Q5939523)

The author studies surfaces in \(\mathbb{R}^N\) with simple geodesics (geodesics of constant Frénet curvatures). The main result is: Let \(F^2\subset\mathbb{R}^N\) be a compact surface with simple geodesics. Then either (1) \(F^2\) is a flat rational torus, or (2) \(F^2\) is the image of the unit sphere in \(\mathbb{R}^3\) under a simple geodesic map. An algorithm for constructing simple geodesic maps is given.