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arXiv · 2609.09750

Product structures and decompositions of $\mathbb{Z}_2\times\mathbb{Z}_2$-symmetric spaces

Jin Matsui
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Abstract

In this paper, we establish the decomposition and product theory of $\Gamma$-symmetric spaces, where $\Gamma$ is isomorphic to $\mathbb{Z}_2\times\mathbb{Z}_2$. These results lead to the local classification of semisimple Riemannian $\mathbb{Z}_2\times\mathbb{Z}_2$-symmetric spaces of nontrivial type. Furthermore, we identify notable phenomena specific to $\mathbb{Z}_2\times\mathbb{Z}_2$-symmetric spaces: the existence of distinct product structures and that of an example with the trivial infinitesimal isotropy representation.

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Jin Matsui. 2026-09-09. Product structures and decompositions of $\mathbb{Z}_2\times\mathbb{Z}_2$-symmetric spaces. https://arxiv.org/abs/2609.09750

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