SO(2)-congruent projections of convex bodies with rotation about the origin
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- by Benjamin Mackey PDF
- Proc. Amer. Math. Soc. 143 (2015), 1739-1744 Request permission
Abstract:
We prove that if two convex bodies $K, L \subset \mathbb {R}^3$ satisfy the property that the orthogonal projections of $K$ and $L$ onto every plane containing the origin are rotations of each other, then either $K$ and $L$ coincide or $L$ is the image of $K$ under a reflection about the origin.References
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Additional Information
- Benjamin Mackey
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- Email: mackeybe@msu.edu
- Received by editor(s): September 18, 2013
- Published electronically: December 9, 2014
- Additional Notes: This research was supported in part by the NSF Grant, DMS-1101636
- Communicated by: Alexander Iosevich
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 1739-1744
- MSC (2010): Primary 52A15
- DOI: https://doi.org/10.1090/S0002-9939-2014-12442-7
- MathSciNet review: 3314085