Isotropy subgroups of some almost rigid domains

Equivalence among isotropy subgroups of space groups.

The Landau theory' of continuous phase transitions provides a powerful tool for understanding transitions between solid phases whose symmetries have a group-subgroup relationship. In the Landau theory, the thermodynamic free energy F of the crystal is written as a function of an order parameter Q. In the high-symmetry phase, the minimum of F is at Q = 0. In the low-symmetry phase, the minimum o...

A Note on Counting Isotropy Subgroups

A general algorithm for generating isotropy subgroups in superspace.

This paper presents a general algorithm for generating the isotropy subgroups of superspace extensions of crystallographic space groups involving arbitrary superpositions of multi-k order parameters from incommensurate and commensurate k vectors. Several examples are presented in detail in order to illuminate each step of the algorithm. The practical outcome is that one can now start with any c...

Nonexistence of Invariant Rigid Structures and Invariant Almost Rigid Structures

We prove that certain volume preserving actions of Lie groups and their lattices do not preserve rigid geometric structures in the sense of Gromov. The actions considered are the ”exotic” examples obtained by Katok and Lewis and the first author, by blowing up closed orbits in the well known actions on homogeneous spaces. The actions on homogeneous spaces all preserve affine connections, wherea...

Meromorphic Almost Rigid Geometric Structures

We study the local Killing Lie algebra of meromorphic almost rigid geometric structures on complex manifolds. This leads to classification results for compact complex manifolds bearing holomorphic rigid geometric structures.