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Vestnik Chelyabinsk. Gos. Univ., 2015, Issue 17, Pages 6–17 (Mi vchgu1)  

This article is cited in 1 scientific paper (total in 1 paper)

Geometry and Topology

Crystal criterion and antipodal Delaunay sets

N. P. Dolbilin

V.A. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russian Federation

Abstract: It is proved that a discrete set of points repeatability local configurations under certain conditions implies the so-called «global order», which includes the presence of a plurality of crystallographic symmetry group. It is also proved that the set of Delaunay, in which all $2R$-clusters are antipodal, that is centrally symmetric, is itself a centrally symmetric with respect to each of its points. Moreover, if in addition to this cluster are identical, then the set is correct, i. e. its symmetry group acts transitively.
This article based on a lecture delivered at the International Conference «Quantum topology» (5-17 July 2014), organized by the Laboratory of Quantum Topology of Chelyabinsk State University.

Keywords: Delaunay set, cluster, the right system, crystallographic group.

Funding Agency Grant Number
Russian Science Foundation 14-11-00414


Full text: PDF file (1191 kB)
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UDC: 514.12
BBK: B121.54

Citation: N. P. Dolbilin, “Crystal criterion and antipodal Delaunay sets”, Vestnik Chelyabinsk. Gos. Univ., 2015, no. 17, 6–17

Citation in format AMSBIB
\Bibitem{Dol15}
\by N.~P.~Dolbilin
\paper Crystal criterion and antipodal Delaunay sets
\jour Vestnik Chelyabinsk. Gos. Univ.
\yr 2015
\issue 17
\pages 6--17
\mathnet{http://mi.mathnet.ru/vchgu1}
\elib{http://elibrary.ru/item.asp?id=23400803}


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    This publication is cited in the following articles:
    1. N. P. Dolbilin, A. N. Magazinov, “Locally antipodal Delaunay sets”, Russian Math. Surveys, 70:5 (2015), 958–960  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
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