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Curved graphite and its mathematical transformations

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Abstract

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.

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  1. Humberto Terrones

    Present address: Instituto de Física, Departamento de Materia Condensada, Universidad Nacional Autónoma de Mexico, Apartado Postal 20-364, C.P. 01000, México, D.F., Mexico

Authors and Affiliations

  1. Department of Crystallography, Birkbeck College, University of London, Malet Street, WC1E7HX, London, UK

    Humberto Terrones

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  1. Humberto Terrones
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Terrones, H. Curved graphite and its mathematical transformations. J Math Chem 15, 143–156 (1994). https://doi.org/10.1007/BF01277556

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  • DOI: https://doi.org/10.1007/BF01277556

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