title: The role of the tangent bundle for symmetry operations and modulated structures.
abstract: 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.
authors.affiliation: Laboratoire de Cristallographie, IPSB-FSB, Ecole Polytechnique Fédérale de Lausanne, Le Cubotron, Dorigny, CH-1015 Lausanne, Switzerland.
authors.forename: Philippe
authors.initials: P
authors.lastname: Kocian
authors.forename: Kurt
authors.initials: K
authors.lastname: Schenk
authors.forename: Gervais
authors.initials: G
authors.lastname: Chapuis