论文标题
旋转组Modulo有限对称性商的局部等距嵌入
Locally Isometric Embeddings of Quotients of the Rotation Group Modulo Finite Symmetries
论文作者
论文摘要
使用基于嵌入的方法对多种有价值数据进行分析与查找合适嵌入的问题有关。在本文中，我们对旋转组Modulo有限对称组的商的嵌入商$ \ mathrm {so}（so}（3）/\ Mathcal {s} $感兴趣。关于这种商歧管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框架，用于构建此类嵌入式，该嵌入物概括了在Arxiv中构建的嵌入：1701.01579。我们较大的嵌入类别的核心优势在于，它包括所有晶体学对称组的等距嵌入。
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.
