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Cusps of Gauss Mappings

by Thomas F. Banchoff, Terence Gaffney, and Clint McCrory

In past papers, Gauss indicated his desire to study the spherical
images of parabolic points of surfaces, that is points where
the Gaussian curvature is zero. Gauss never published any results
in this regard, and so this paper examines parabolic points and
cusps of Gauss mappings. In particular, we give ten geometric
characterizaions of cusps of Gauss mappings, a discussion of
elliptic and hyperbolic cusps, and applications of singularity
theory to differential geometry.