The role of the tangent bundle for symmetry operations and modulated structures
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The subject of this thesis lies in the intersection of differential geometry and functional analysis, a domain usually called global analysis. A central object in this work is the group Ds(M) of all orientation preserving diffeomorphisms of a compact manif ...
The space-group symmetry of a crystal structure imposes a point-group symmetry on its diffraction pattern, giving rise to so-called symmetry-equivalent reflections. Instances in macromolecular crystallography are discussed in which the symmetry in reciproc ...
The mathematical facet of modern crystallography is essentially based on analytical geometry, linear algebra as well as group theory. This study endeavours to approach the geometry and symmetry of crystals using the tools furnished by differential geometry ...
The construction of low-dimensional models explaining high-dimensional signal observations provides concise and efficient data representations. In this paper, we focus on pattern transformation manifold models generated by in-plane geometric transformation ...
The rapid development of the Internet has created new opportunities for teaching in general and it is our aim to show how the current evolution can best be exploited for crystallography education in particular. Currently, we can find a very large selection ...
We study periodic torus orbits on spaces of lattices. Using the action of the group of adelic points of the underlying tori, we define a natural equivalence relation on these orbits, and show that the equivalence classes become uniformly distributed. This ...
A general formalism for the maximal symmetrization and reduction of fields (MSRFs) is proposed and applied to wave functions in solid-state nanostructures. Its primary target is to provide an essential tool for the study and analysis of the electronic and ...
We obtain a theory of stratified Sternberg spaces thereby extending the theory of cotangent bundle reduction for free actions to the singular case where the action on the base manifold consists of only one orbit type. We find that the symplectic reduced sp ...
The low-temperature structure of 4-methylpyridine-N-oxide was previously determined in symmetry P4(1) [Damay et al. (2006), Acta Cryst. B62, 627-633]. Using a recently published symmetry-determination method it was found that the true symmetry of the struc ...
Differential geometry provides a useful mathematical framework for describing the fundamental concepts in crystallography. The notions of point and associated vector spaces correspond to those of manifold and tangent space at a given point. A space-group o ...
