Symplectic critical surfaces in Kähler surfaces
| dc.creator | Han, Xiaoli | |
| dc.creator | Li, Jiayu | |
| dc.date | 2007-11-14 | |
| dc.date.accessioned | 2026-07-07T08:42:56Z | |
| dc.date.available | 2026-07-07T08:42:56Z | |
| dc.description | Let $M$ be a Kähler surface and $Σ$ be a closed symplectic surface which is smoothly immersed in $M$. Let $α$ be the Kähler angle of $Σ$ in $M$. We first deduce the Euler-Lagrange equation of the functional $L=\int_Σ\frac{1}{\cosα}dμ$ in the class of symplectic surfaces. It is $\cos^3αH=(J(J\nabla\cosα)^\top)^\bot$, where $H$ is the mean curvature vector of $Σ$ in $M$, $J$ is the complex structure compatible with the Kähler form $ω$ in $M$, which is an elliptic equation. We then study the properties of the equation. | |
| dc.identifier | https://arxiv.org/abs/0711.2211 | |
| dc.identifier | http://arxiv.org/abs/0711.2211 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142143 | |
| dc.subject | Differential Geometry | |
| dc.subject | Symplectic Geometry | |
| dc.title | Symplectic critical surfaces in Kähler surfaces | |
| dc.type | text |