论文标题
三维晶格的完整轴测分类
A complete isometry classification of 3-dimensional lattices
论文作者
论文摘要
欧几里得3空间中的周期性晶格是基矢量的所有整数线性组合的无限集。任何晶格都可以通过无限的许多不同的基础产生。这种歧义仅是部分解决的，但是在对晶体振动建模的扰动下，标准降低仍然不连续。本文完成了3维晶格的连续分类，直至欧几里得等轴测图（或一致性）和相似性（具有均匀的缩放）。新的同质不变式是四个SuperBase vectors的标量量表的正方形根，其四个SuperBase Vectors sum sum sum as Sum为零，并且所有成对的All Pairwwise Angles is banepwise Anguce is n nas-canles is bes in-cane is cant is is superbase vectors。这些根源不变板在基础向量的扰动下不断变化。几何方法扩展了DeLone，Conway和Sloane的工作。
A periodic lattice in Euclidean 3-space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard reductions remained discontinuous under perturbations modelling crystal vibrations. This paper completes a continuous classification of 3-dimensional lattices up to Euclidean isometry (or congruence) and similarity (with uniform scaling).The new homogeneous invariants are uniquely ordered square roots of scalar products of four superbase vectors whose sum is zero and all pairwise angles are non-acute. These root invariants continuously change under perturbations of basis vectors. The geometric methods extend the work of Delone, Conway and Sloane.
