三维格的完全isometry分类
A complete isometry classification of 3-dimensional lattices
摘要：
欧氏空间中的周期格是基向量的所有整数线性组合的无限集。任何格都可以由无穷多个不同的基生成。这种模糊性只是部分解决，但标准的减少仍然不连续的扰动下模拟晶体振动。本文对三维格进行了直到欧氏等距（或同余）和相似（具有一致标度）的连续分类，新的齐次不变量是四个和为零且两两夹角均为非锐角的超基向量的标积的唯一有序平方根.这些根不变量在基向量的扰动下连续变化。几何方法推广了Delone，Conway和Sloane的工作.
英文摘要：
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.
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