# Characterizing singularities of a surface in Lie sphere geometry

@article{Pember2017CharacterizingSO, title={Characterizing singularities of a surface in Lie sphere geometry}, author={Mason Pember and Wayne Rossman and Kentaro Saji and Keisuke Teramoto}, journal={Hokkaido Mathematical Journal}, year={2017} }

The conditions for a cuspidal edge, swallowtail and other fundamental singularities are given in the context of Lie sphere geometry. We then use these conditions to study the Lie sphere transformations of a surface.

## References

SHOWING 1-10 OF 33 REFERENCES

### Singularities of improper affine spheres and surfaces of constant Gaussian curvature

- Mathematics
- 2005

We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singlarities appearing in geometric solutions to the…

### Singularities of parallel surfaces

- Mathematics
- 2012

We investigate singularities of all parallel surfaces to a given regular surface. In generic context, the types of singularities of parallel surfaces are cuspidal edge, swallowtail, cuspidal lips,…

### Singularities of the asymptotic completion of developable M

- Mathematics
- 2010

We prove that the asymptotic completion of a developable Mobius strip in Euclidean three-space must have at least one singular point other than cuspidal edge singularities. Moreover, if the strip is…

### Maximal surfaces with singularities in Minkowski space

- Mathematics
- 2003

We shall investigate maximal surfaces in Minkowski 3-space with singularities. Although the plane is the only complete maximal surface without singular points, there are many other complete maximal…

### Principal curvatures and parallel surfaces of wave fronts

- MathematicsAdvances in Geometry
- 2019

Abstract We give criteria for which a principal curvature becomes a bounded C∞-function at non-degenerate singular points of wave fronts by using geometric invariants. As applications, we study…

### ANALOG OF WILCZYNSKI'S PROJECTIVE FRAME IN LIE SPHERE GEOMETRY: LIE-APPLICABLE SURFACES AND COMMUTING SCHRÖDINGER OPERATORS WITH MAGNETIC FIELDS

- Mathematics
- 2002

We propose a construction of surfaces in Lie sphere geometry based on the linear system which copies equations of Wilczynski's projective frame. In the particular case of Lie-applicable surfaces this…

### Singularities of flat fronts in hyperbolic space

- Mathematics
- 2004

It is well-known that the unit cotangent bundle of any Riemannian manifold has a canonical contact structure. A surface in a Riemannian 3-manifold is called a front if it is the projection of a…