Journal of Mathematical Chemistry

, Volume 15, Issue 1, pp 143–156

Curved graphite and its mathematical transformations

  • Humberto Terrones

DOI: 10.1007/BF01277556

Cite this article as:
Terrones, H. J Math Chem (1994) 15: 143. doi:10.1007/BF01277556


Mathematical transformations for graphite with positive, negative and zero Gaussian curvatures are presented. When the Gaussian curvatureK is zero, we analyse a bending transformation from a planar sheet into a cone. The Bonnet, the Goursat and a mixed transformation are studied for graphitic structures with the same topologies as triply periodic minimal surfaces (K < 0). We have found that using the Kenmotsu equations for surfaces of constant mean curvature it is possible to invert spherical and cylindrical graphite. A bending transformation for surfaces of revolution is also studied; during this transformation the helical arrangement of cylinders changes. All these transformations can give an insight into kinematic processes of curved graphite and into new shapes.

Copyright information

© J.C. Baltzer AG, Science Publishers 1994

Authors and Affiliations

  • Humberto Terrones
    • 1
  1. 1.Department of CrystallographyBirkbeck College, University of LondonLondonUK
  2. 2.Instituto de Física, Departamento de Materia CondensadaUniversidad Nacional Autónoma de MexicoMéxico, D.F.Mexico