Principal curvatures and parallel surfaces of wave fronts
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Keisuke Teramoto
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 singularities of parallel surfaces and extended distance squared functions of wave fronts. Moreover, we relate these singularities to some geometric invariants of fronts.
Acknowledgements
The author thanks Professor Kentaro Saji for fruitful discussions and valuable comments. He also thanks the referee for reading the manuscript carefully and for helpful suggestions.
Communicated by: P. Eberlein
Funding The author was partly supported by the Grant-in-Aid for JSPS Fellows, No. 17J02151.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A Batyrev type classification of ℚ-factorial projective toric varieties
- Blocking sets of certain line sets related to a hyperbolic quadric in PG(3, q)
- Affine-compact functors
- Limit points of the branch locus of 𝓜g
- Criteria for strict monotonicity of the mixed volume of convex polytopes
- Principal curvatures and parallel surfaces of wave fronts
- Nodal curves with a contact-conic and Zariski pairs
- Corrigendum to the paper “On surfaces with two apparent double points”
Articles in the same Issue
- Frontmatter
- A Batyrev type classification of ℚ-factorial projective toric varieties
- Blocking sets of certain line sets related to a hyperbolic quadric in PG(3, q)
- Affine-compact functors
- Limit points of the branch locus of 𝓜g
- Criteria for strict monotonicity of the mixed volume of convex polytopes
- Principal curvatures and parallel surfaces of wave fronts
- Nodal curves with a contact-conic and Zariski pairs
- Corrigendum to the paper “On surfaces with two apparent double points”
