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A Short Lecture on Topological Crystallography and a Discrete Surface Theory

Differential Geometry 2020-02-25 v1 Mathematical Physics math.MP

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 33-dimensional Euclidean space, which are mathematical models of crystal/molecular structures.

Keywords

Cite

@article{arxiv.2002.09562,
  title  = {A Short Lecture on Topological Crystallography and a Discrete Surface Theory},
  author = {Hisashi Naito},
  journal= {arXiv preprint arXiv:2002.09562},
  year   = {2020}
}

Comments

44 pages, 38 figures, and 1 table. available at http://math.korea.ac.kr/_res/math/etc/AnamLectureNotesVol2_20200210.pdf

R2 v1 2026-06-23T13:50:00.051Z