Axial Presentations of Regular Arcs on M(n).
THEOREM 1. Let M(n) be a Riemannian manifold of class C(m), m > 0. On M(n) let g be a simple compact, sensed, regular arc whose local coordinates are functions of class C(m) of the algebraic arc length s, measured along g from a prescribed point of g. There then exists a presentation (F: U, X) [unk] [unk]M(n) such that g [unk] X, and each point p(s) of g is represented in the euclidean domain U by coordinates (x(1),...,x(n)) = (s,0,...,0).
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Institute for Advanced Study, Princeton, New Jersey 08540.