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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2511.17495 |
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- This paper provides a classification of analytic actions of the semi-orthogonal group $\text{SO}^\circ(p,q)$, for $p,q \geq 3$, on closed, connected $(p+q-1)$-dimensional manifolds. Adapting Uchida's construction of $\text{SO}^\circ(p,q)$ actions on $\text{S}^{p+q-1}$, we explicitly construct analytic actions of $\text{SO}^\circ(p,q)$ on $\text{S}^{p} \times \text{S}^{q-1}$ and $\text{S}^{p-1} \times \text{S}^{q}$, as well as actions on $\text{SO}^\circ(p,q) \times_P \text{S}^1$, where $P$ is a maximal parabolic subgroup of $\text{SO}^\circ(p,q)$. The main result demonstrates that any analytic $\text{SO}^\circ(p,q)$ action on a closed, connected $(p+q-1)$-dimensional manifold is covered by one of the constructed actions.