旋转群模有限对称商的局部等距嵌入
Locally Isometric Embeddings of Quotients of the Rotation Group Modulo Finite Symmetries
摘要：
使用基于嵌入的方法分析流形值数据与找到合适嵌入的问题有关。本文主要研究旋转群模有限对称群的商流形$\mathrm{SO}(3)/\mathcal{S}$的嵌入问题。关于这种商流形的数据自然出现在晶体学、材料科学和生物化学中。我们提供了一个通用的框架，用于构建这样的嵌入，它概括了在arXiv：1701.01579中构建的嵌入。我们更大的嵌入类的核心优势是，它包括所有晶体学对称群的等距嵌入。
英文摘要：
The analysis of manifold valued data using embedding based methods is linked to the problem of finding suitable embeddings. In this paper we are interested in embeddings of quotient manifolds $\mathrm{SO}(3)/\mathcal{S}$ of the rotation group modulo finite symmetry groups. Data on such quotient manifolds naturally occur in crystallography, material science and biochemistry. We provide a generic framework for the construction of such embeddings which generalizes the embeddings constructed in arXiv:1701.01579. The central advantage of our larger class of embeddings is that it comprises isometric embeddings for all crystallographic symmetry groups.
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