Parallel and dual surfaces of cuspidal edges
arXiv:1510.06500 · doi:10.1016/j.difgeo.2015.10.005
Abstract
We study parallel surfaces and dual surfaces of cuspidal edges. We give concrete forms of principal curvature and principal direction for cuspidal edges. Moreover, we define ridge points for cuspidal edges by using those. We clarify relations between singularities of parallel and dual surfaces and differential geometric properties of initial cuspidal edges.
9 pages, 2 figures
References in corpus (1)
Cited by in corpus (11)
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- Focal surfaces of wave fronts in the Euclidean 3-space
- On the flat geometry of the cuspidal edge
- Discrete linear Weingarten surfaces with singularities in Riemannian and Lorentzian spaceforms
- Geometric invariants of cuspidal edges
- Behavior of principal curvatures of frontals near non-front singular points and their application
- Extendibility and boundedness of invariants on singularities of wavefronts
- On Gaussian curvatures and singularities of Gauss maps of cuspidal edges
- On pairs of geometric foliations on a cuspidal edge
- Characterizing singularities of a surface in Lie sphere geometry
- On the geometry of folded cuspidal edges