A Short Lecture on Topological Crystallography and a Discrete Surface Theory

Authors :: Naito, Hisashi
Source :: Anam Lecture Notes in Mathematics, An introduction to discrete differential geometry, Volume 2, 83-147 (2020)
Publication Year :: 2020
Abstract: This is an unrefereed lecture note based on lectures in 'Introductory Workshop on Discrete Differential Geometry' at Korea University on January 21--24, 2019. In this note, we discuss topological crystallography, which is a mathematical theory of crystal structures. The most symmetric structure among all placements of the graph is obtained by a variational principle in topological crystallography. We also discuss a theory of trivalent discrete surfaces in $3$-dimensional Euclidean space, which are mathematical models of crystal/molecular structures.<br />Comment: 44 pages, 38 figures, and 1 table. available at http://math.korea.ac.kr/_res/math/etc/AnamLectureNotesVol2_20200210.pdf

Database :: arXiv
Journal :: Anam Lecture Notes in Mathematics, An introduction to discrete differential geometry, Volume 2, 83-147 (2020)
Publication Type :: Report
Accession number :: edsarx.2002.09562
Document Type :: Working Paper

Tools