Polar actions on compact Euclidean hypersurfaces
| dc.creator | Moutinho, Ion | |
| dc.creator | Tojeiro, Ruy | |
| dc.date | 2007-04-13 | |
| dc.date.accessioned | 2026-07-07T07:56:34Z | |
| dc.date.available | 2026-07-07T07:56:34Z | |
| dc.description | Given an isometric immersion $f\colon M^n\to \R^{n+1}$ of a compact Riemannian manifold of dimension $n\geq 3$ into Euclidean space of dimension $n+1$, we prove that the identity component $Iso^0(M^n)$ of the isometry group $Iso(M^n)$ of $M^n$ admits an orthogonal representation $Φ\colon Iso^0(M^n)\to SO(n+1)$ such that $f\circ g=Φ(g)\circ f$ for every $g\in Iso^0(M^n)$. If $G$ is a closed connected subgroup of $Iso(M^n)$ acting locally polarly on $M^n$, we prove that $Φ(G)$ acts polarly on $\R^{n+1}$, and we obtain that $f(M^n)$ is given as $Φ(G)(L)$, where $L$ is a hypersurface of a section which is invariant under the Weyl group of the $Φ(G)$-action. We also find several sufficient conditions for such an $f$ to be a rotation hypersurface. Finally, we show that compact Euclidean rotation hypersurfaces of dimension $n\geq 3$ are characterized by their underlying warped product structure. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0704.1807 | |
| dc.identifier | http://arxiv.org/abs/0704.1807 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127355 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53 A07, 53 C40, 53 C42 | |
| dc.title | Polar actions on compact Euclidean hypersurfaces | |
| dc.type | text |