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

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...

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Bibliographic Details
Published in:Journal of multivariate analysis 2021-09, Vol.185, p.104764, Article 104764
Main Authors: Hielscher, Ralf, Lippert, Laura
Format: Article
Language:English
Subjects:
Euclidean embedding
Locally isometric embedding
Rotation group
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Summary: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.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2021.104764