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Product structures and decompositions of ℤ2×ℤ2-symmetric spaces

  • Jin Matsui
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Abstract

In this paper, we establish the decomposition and product theory of Γ-symmetric spaces, where Γ is isomorphic to ℤ2×ℤ2. These results lead to the local classification of semisimple Riemannian ℤ2×ℤ2-symmetric spaces of nontrivial type. Furthermore, we identify notable phenomena specific to ℤ2×ℤ2-symmetric spaces: the existence of distinct product structures and that of an example with the trivial infinitesimal isotropy representation.

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Cite

BibTeXRIS
BibTeX
@misc{matsui2026product,
  title = {{Product structures and decompositions of $\mathbbZ_2\times\mathbbZ_2$-symmetric spaces}},
  author = {Jin Matsui},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09750},
  eprint = {2609.09750},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09750},
}
RIS
TY  - UNPB
TI  - Product structures and decompositions of ℤ_2×ℤ_2-symmetric spaces
AU  - Jin Matsui
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.09750
UR  - https://arxiv.org/abs/2609.09750
AB  - In this paper, we establish the decomposition and product theory of Γ-symmetric spaces, where Γ is isomorphic to ℤ_2×ℤ_2. These results lead to the local classification of semisimple Riemannian ℤ_2×ℤ_2-symmetric spaces of nontrivial type. Furthermore, we identify notable phenomena specific to ℤ_2×ℤ_2-symmetric spaces: the existence of distinct product structures and that of an example with the trivial infinitesimal isotropy representation.
ER  -