On C2 -smooth Surfaces of Constant Width

Authors

Brendan Guilfoyle, School of Science, Technology, Engineering and Mathematics, Institute of Technology, Tralee, Clash, Tralee, Co. Kerry, Ireland.Follow
Wilhelm Klingenberg, Department of Mathematical Sciences, University of Durham

ORCID

0000-0002-7437-5046

Document Type

Article

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Disciplines

Mathematics | Physical Sciences and Mathematics

Publication Details

Tblisi Mathetmatical Journal, vol. 2. © 2009 Tbilisi Centre for Mathematical Sciences

Abstract

A number of results for C2 -smooth surfaces of constant width in Euclidean 3-space E 3 are obtained. In particular, an integral inequality for constant width surfaces is established. This is used to prove that the ratio of volume to cubed width of a constant width surface is reduced by shrinking it along its normal lines. We also give a characterization of surfaces of constant width that have rational support function. Our techniques, which are complex differential geometric in nature, allow us to construct explicit smooth surfaces of constant width in E 3 , and their focal sets. They also allow for easy construction of tetrahedrally symmetric surfaces of constant width.

Recommended Citation

Brendan Guilfoyle. Wilhelm Klingenberg. "On C2-smooth Surfaces of Constant Width." Tbilisi Math. J. 2 1 - 17, 2009. https://doi.org/10.32513/tbilisi/1528768838