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 $\mathrm{SO}\left(3\right)∕\mathcal{S}$ 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 Arnold et al. (2018). The central advantage of our larger class of embeddings is that it includes locally isometric embeddings for all crystallographic symmetry groups.

中文翻译：

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旋转群模有限对称的商的局部等距嵌入

使用基于嵌入的方法对流形值数据进行分析与找到合适的嵌入问题有关。在本文中，我们对商流形的嵌入感兴趣$\mathrm{所以}（3）∕\mathcal{小号}$旋转群的模有限对称群。关于这种商流形的数据自然存在于晶体学，材料科学和生物化学中。我们提供了用于构建此类嵌入的通用框架，该框架对在Arnold等人中构建的嵌入进行了概括。（2018）。我们较大类型的嵌入的主要优势在于，它包括所有晶体对称组的局部等距嵌入。