Guardado en:
Detalles Bibliográficos
Autor principal: Lentas, Spyridon
Formato: Preprint
Publicado: 2025
Materias:
Acceso en línea:https://arxiv.org/abs/2511.17495
Etiquetas: Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
_version_ 1866914166642573312
author Lentas, Spyridon
author_facet Lentas, Spyridon
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_17495
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Classification of analytic $\text{SO}^\circ(p,q)$-actions on closed $(p+q-1)$-dimensional manifolds I : $p, q \geq 3$
Lentas, Spyridon
Differential Geometry
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.
title Classification of analytic $\text{SO}^\circ(p,q)$-actions on closed $(p+q-1)$-dimensional manifolds I : $p, q \geq 3$
topic Differential Geometry
url https://arxiv.org/abs/2511.17495