Willmore submanifolds in a sphere
| dc.creator | Li, Haizhong | |
| dc.date | 2002-10-16 | |
| dc.date.accessioned | 2026-07-07T04:52:00Z | |
| dc.date.available | 2026-07-07T04:52:00Z | |
| dc.description | Let $x:M\to S^{n+p}$ be an $n$-dimensional submanifold in an $(n+p)$-dimensional unit sphere $S^{n+p}$, $x:M\to S^{n+p}$ is called a Willmore submanifold to the following Willmore functional: $$ \int_M(S-nH^2)^{\frac{n}{2}}dv, $$ where $S=\sum\limits_{α,i,j}(h^α_{ij})^2$ is the square of the length of the second fundamental form, $H$ is the mean curvature of $M$. In [13], author proved an integral inequality of Simon's type for $n$-dimensional compact Willmore hypersurfaces in $S^{n+1}$ and gave a characterization of {\it Willmore tori}. In this paper, we generalize this result to $n$-dimensional compact Willmore submanifolds in $S^{n+p}$. In fact, we obtain an integral inequality of Simon's type for compact Willmore submanifolds in $S^{n+p}$ and give a characterization of {\it willmore tori} and {\it Veronese surface} by use of integral inequality. | |
| dc.description | 18 pages. To appear in Mathematical Research Letter | |
| dc.identifier | https://arxiv.org/abs/math/0210239 | |
| dc.identifier | http://arxiv.org/abs/math/0210239 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65309 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C42; 53A10 | |
| dc.title | Willmore submanifolds in a sphere | |
| dc.type | text |