A mean-curvature flow along a Kahler-Ricci flow

doi:10.1142/S0129167X18500064

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	A mean-curvature flow along a Kahler-Ricci flow
	Han, Xiaoli 1; Li, Jiayu2,3 ; Zhao, Liang 4
	2018
发表期刊	INTERNATIONAL JOURNAL OF MATHEMATICS
ISSN	0129-167X
卷号	29 期号:1 页码:25
摘要	Let (M, (g) over bar) be a Kahler surface, and S an immersed surface in M. The Kahler angle of S inM is introduced by Chern andWolfson [Am. J. Math. 105 (1983) 59-83]. Let (M, (g) over bar (t)) evolve along the Kahler- Ricci flow, and Sigma t in (M, (g) over bar (t)) evolve along the mean- curvature flow. We show that the Kahler angle alpha(t) satisfies the evolution equation (partial derivative/partial derivative(t) - Delta) cos alpha = \|(del) over bar J Sigma(t)\|(2) cos alpha +Rsin(2) alpha cos alpha, where R is the scalar curvature of (M, (g) over bar (t)). The equation implies that if the initial surface is symplectic (Lagrangian), then, along the flow, St is always symplectic (Lagrangian) at each time t, which we call a symplectic (Lagrangian) Kahler-Ricci mean-curvature flow. In this paper, we mainly study the symplectic Kahler-Ricci mean-curvature flow.
关键词	Kahler angle Kahler-Ricci flow mean-curvature flow symplectic surface
DOI	10.1142/S0129167X18500064
语种	英语
资助项目	NSF in China[11131007] ; NSF in China[11471014] ; NSF in China[11201028]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000423846000006
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29443
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.Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China 3.AMSS CAS, Beijing 100190, Peoples R China 4.Beijing Normal Univ, MOE, LMCS, Sch Math Sci, Beijing 100875, Peoples R China
推荐引用方式 GB/T 7714	Han, Xiaoli,Li, Jiayu,Zhao, Liang. A mean-curvature flow along a Kahler-Ricci flow[J]. INTERNATIONAL JOURNAL OF MATHEMATICS,2018,29(1):25.
APA	Han, Xiaoli,Li, Jiayu,&Zhao, Liang.(2018).A mean-curvature flow along a Kahler-Ricci flow.INTERNATIONAL JOURNAL OF MATHEMATICS,29(1),25.
MLA	Han, Xiaoli,et al."A mean-curvature flow along a Kahler-Ricci flow".INTERNATIONAL JOURNAL OF MATHEMATICS 29.1(2018):25.