Pairs of Convex Bodies with Centrally
Symmetric Intersections of Translates |
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Authors: | Valeriu Soltan |
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Institution: | (1) Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, VA 22030-4444, USA |
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Abstract: | For a pair of convex bodies $K$ and $K $ in $E^d$,
the $d$-dimensional intersections $K \cap (x + K ),$ $x \in E^d,$
are centrally symmetric if and only if $K$ and $K $ are
represented as direct sums $K = R \oplus P$ and $K = R \oplus
P $ such that: (i) $R$ is a compact convex set of some dimension
$m$, $0 \le m \le d,$ and $R = z - R$ for a suitable vector $z
\in E^d$, (ii) $P$ and $P $ are isothetic parallelotopes, both of
dimension $d-m$. |
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Keywords: | |
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