Properties of parallel-surfaces coordinate systems (Q1057138)

The coordinate systems in \(E_ 3\) are studied, having the Euclidean distance from S (a surface in \(E_ 3)\) as one of the coordinates, in order to exploit the particular role played by a direction field (the normal to S) in some fluid dynamic problems. In such coordinate systems, the normal scalar components will be invariant. The author shows that only in such systems (called parallel-surfaces coordinate systems) this property holds. A number of applications to fluid mechanics are given in other papers of the author [see e.g.: Acta Astronaut. 5, 655-670 (1978; Zbl 0398.76007)].