On geodesics of framed surfaces in the Euclidean 3-space (Q6589767)

In this paper, the author defines the notion of geodesics for surfaces with singular points. Geodesics are important in a great many areas of science: differential geometry, physics, architecture and computer science. A geodesic is a regular curve representing in some sense the shortest path between two points in a regular surface. In order to extend the definition of geodesics for surfaces with singular points, the author uses an extension of the notion that ``the tangential component of the acceleration of the curve vanishes''. As surfaces with singular points, he considers framed surfaces and as curves with singular points, framed curves. Furthermore, some properties of geodesics are investigated and examples are presented.