ON THE THEORY OF FRONTS ON THE 2-SPHERE AND THE THEORY OF SPACE CURVES

摘要

We apply the singularity theory of caustics and wave fronts on the 2-sphere and the theory of Legendrian curves of the (contact) manifold ST*S~2 ～ RP~3 (consisting of tangent contact elements of the sphere S2) to obtain new results in the theory of curves in the Euclidean 3-space. In this way, the singularity theory of caustics and wave fronts provides a new insight to the differential geometry of curves in the Euclidean 3-space.