Giblin, Peter and Reeve, Graham and Uribe-Vargas, Ricardo (2021) Contact with circles and Euclidean invariants of surfaces in three space. The Quarterly Journal of Mathematics. ISSN 0033-5606 (Accepted for Publication)
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Abstract
We investigate the vertex curve, that is the set of points in the hyperbolic region of a smooth surface in real 3-space at which there is a circle in the tangent plane having at least 5-point contact with the surface. The vertex curve is related to the differential geometry of planar sections of the surface parallel to and close to the tangent planes, and to the symmetry sets of isophote curves, that is level sets of intensity in a 2-dimensional image. We investigate also the relationship of the vertex curve with the parabolic and flecnodal curves, and the evolution of the vertex curve in a generic 1-parameter family of smooth surfaces.
| Item Type: | Article |
|---|---|
| Additional Information and Comments: | © The Author(s) 2021. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. The final, published version will be available from: https://doi.org/10.1093/qmath/haab058 |
| Faculty / Department: | Faculty of Human and Digital Sciences > Mathematics and Computer Science |
| Depositing User: | Graham Reeve |
| Date Deposited: | 10 Feb 2022 10:09 |
| Last Modified: | 31 May 2022 00:15 |
| URI: | https://hira.hope.ac.uk/id/eprint/3485 |
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