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SO(2)-congruent projections of convex bodies with rotation about the origin


Author: Benjamin Mackey
Journal: Proc. Amer. Math. Soc. 143 (2015), 1739-1744
MSC (2010): Primary 52A15
Published electronically: December 9, 2014
MathSciNet review: 3314085
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

Benjamin Mackey
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: mackeybe@msu.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12442-7
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
Article copyright: © Copyright 2014 American Mathematical Society