Symplectic critical surfaces in Kahler surfaces
文献类型：期刊论文
| 作者 | Han, Xiaoli1; Li, Jiayu2,3
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| 刊名 | JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
 |
| 出版日期 | 2010 |
| 卷号 | 12期号:2页码:505-527 |
| 关键词 | Symplectic surface holomorphic curve Kahler surface |
| ISSN号 | 1435-9855 |
| DOI | 10.4171/JEMS/207 |
| 英文摘要 | Let M be a Kahler surface and Sigma be a closed symplectic surface which is smoothly immersed in M. Let alpha be the Kahler angle of Sigma in M. We first deduce the Euler-Lagrange equation of the functional L = integral(Sigma) = 1/cos alpha d mu in the class of symplectic surfaces. It is cos(3) alpha H = (J(J del cos alpha)(inverted perpendicular))(perpendicular to), where H is the mean curvature vector of Sigma in M, and J is the complex structure compatible with the Kahler form omega in M; it is an elliptic equation. We call a surface satisfying this equation a symplectic critical surface. We show that, if M is a Kahler - Einstein surface with nonnegative scalar curvature, each symplectic critical surface is holomorphic. We also study the topological properties of symplectic critical surfaces. By our formula and Webster's formula, we deduce that the Kahler angle of a compact symplectic critical surface is constant, which is not true for noncompact symplectic critical surfaces. |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000275735300010 |
| 出版者 | EUROPEAN MATHEMATICAL SOC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/9720]  |
| 专题 | 数学所 |
| 通讯作者 | Han, Xiaoli |
| 作者单位 | 1.Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China 2.Abdus Salam Int Ctr Theoret Phys, Math Grp, I-34100 Trieste, Italy 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Han, Xiaoli,Li, Jiayu. Symplectic critical surfaces in Kahler surfaces[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY,2010,12(2):505-527. |
| APA | Han, Xiaoli,&Li, Jiayu.(2010).Symplectic critical surfaces in Kahler surfaces.JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY,12(2),505-527. |
| MLA | Han, Xiaoli,et al."Symplectic critical surfaces in Kahler surfaces".JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 12.2(2010):505-527. |
入库方式： OAI收割
来源：数学与系统科学研究院
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