Symplectic critical surfaces in Kahler surfaces

doi:10.4171/JEMS/207

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	Symplectic critical surfaces in Kahler surfaces
	Han, Xiaoli 1; Li, Jiayu2,3
	2010
发表期刊	JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
ISSN	1435-9855
卷号	12 期号:2 页码:505-527
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.
关键词	Symplectic surface holomorphic curve Kahler surface
DOI	10.4171/JEMS/207
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000275735300010
出版者	EUROPEAN MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/9721
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.