Locally isometric embeddings of quotients of the rotation group modulo finite symmetries

JOURNAL OF MULTIVARIATE ANALYSIS

卷:185

Article

Hielscher, Ralf¹  Lippert, Laura¹ 

[1] Tech Univ Chemnitz, Fac Math, Chemnitz, Germany

关键词: Euclidean embedding;    Locally isometric embedding;    Rotation group;   

DOI  :  10.1016/j.jmva.2021.104764

来源: Elsevier

【 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 SO(3)/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. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free