Publications related to Differential geometry: a natural tool for describing symmetry operations

Broken symmetries in macromolecular crystallography: phasing from unmerged data

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 ...

International Union of Crystallography2010

Maximal symmetrization and reduction of fields: Application to wave functions in solid-state nanostructures

Marc-André Dupertuis, Sascha Dalessi

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 ...

2010

Obtaining molecular orientation from second harmonic and sum frequency scattering experiments in water: angular distribution and polarization dependence

Sylvie Roke

We present a method for determining molecular orientation from second-order nonlinear light scattering experiments. Our modeling shows that there is an optimal angular region, for which the scattering pattern is most sensitive to molecular orientation. We ...

2010

Differential geometry applied to crystallography

Philippe Kocian

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 ...

EPFL2009

Infinite dimensional geodesic flows and the universal Teichmüller space

François Gay-Balmaz

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 ...

EPFL2009

Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

Marc Troyanov

David Hilbert discovered in 1895 an important metric that is canonically associated to any convex domain

\Omega

in the Euclidean (or projective) space. This metric is known to be Finslerian, and the usual proof assumes a certain degree of smoothness of t ...

2009

Isometry groups of non-positively curved spaces: Structure Theory

Nicolas Monod

We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric spaces and Bruhat- ...

2009

Closedness of the Tangent Spaces to the Orbits of Proper Actions

Madeleine Jotz

In this note we show that, for any proper action of a Banach-Lie group G on a Banach manifold M, the corresponding tangent maps g -> T-x(M) have closed range for each x is an element of M, i.e., the tangent spaces of the orbits are closed. As a consequence ...

2008

Symmetry determination following structure solution in P1

A new method for space-group determination is described. It is based on a symmetry analysis of the structure-factor phases resulting from a structure solution in space group P1. The output of the symmetry analysis is a list of all symmetry operations compa ...

2008

The symplectic normal space of a cotangent-lifted action

For the cotangent bundle T*Q of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal space at any point. We show that this space splits as the direct sum of th ...

2008

Differential geometry: a natural tool for describing symmetry operations

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Broken symmetries in macromolecular crystallography: phasing from unmerged data

Maximal symmetrization and reduction of fields: Application to wave functions in solid-state nanostructures

Obtaining molecular orientation from second harmonic and sum frequency scattering experiments in water: angular distribution and polarization dependence

Differential geometry applied to crystallography

Infinite dimensional geodesic flows and the universal Teichmüller space

Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

Isometry groups of non-positively curved spaces: Structure Theory

Closedness of the Tangent Spaces to the Orbits of Proper Actions

Symmetry determination following structure solution in P1

The symplectic normal space of a cotangent-lifted action

Differential geometry applied to crystallography

Broken symmetries in macromolecular crystallography: phasing from unmerged data

Symmetry determination following structure solution in P1

The symplectic normal space of a cotangent-lifted action

Harmonic symmetrization of convex sets and of Finsler structures, with applications to Hilbert geometry

Closedness of the Tangent Spaces to the Orbits of Proper Actions

Maximal symmetrization and reduction of fields: Application to wave functions in solid-state nanostructures

Obtaining molecular orientation from second harmonic and sum frequency scattering experiments in water: angular distribution and polarization dependence

Infinite dimensional geodesic flows and the universal Teichmüller space

Isometry groups of non-positively curved spaces: Structure Theory