Year: 2026
Type: preprint
Abstract: In this paper, we establish the decomposition and product theory of $Γ$-symmetric spaces, where $Γ$ 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.
Source: arXiv (Cornell University)
Author: Matsui, Jin
Institution: Tokyo Metropolitan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212137318