The role of the tangent bundle for symmetry operations and modulated structures

• Published in: Acta Crystallographica Section a Crystal Physics Diffraction Theoretical and General Crystallography (ISSN: 0567-7394), vol. A66, p. 394–406
• Publication date: 2010

An equivalence relation on the tangent bundle of a manifold is defined in order to extend a structure (modulated or not) onto it. This extension affords a representation of a structure in any tangent space and that in another tangent space can easily be derived. Euclidean symmetry operations associated with the tangent bundle are generalized and their usefulness for the determination of the intrinsic translation part in helicoidal axes and glide planes is illustrated. Finally, a novel representation of space groups is shown to be independent of any origin point.

Keywords: tengent bundle ; differntial geometry ; symmetry operations ; modulated structures

Reference

• EPFL-ARTICLE-149401
• doi:10.1107/S010876730905226X
• View record in Web of Science

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Record created on 2010-06-17, modified on 2012-03-21