A mean-curvature flow along a Kahler-Ricci flow
A mean-curvature flow along a Kahler-Ricci flow
复制标题
沿 Kahler-Ricci 流的平均曲率流
DOI：
10.1142/s0129167x18500064
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发表时间：
2018-01-01
影响因子：
0.6
通讯作者：
Zhao, Liang
中科院分区：
文献类型：
--
作者：
Han, Xiaoli;Li, Jiayu;Zhao, Liang
设（M，（g）over bar）为Kahler曲面，S为M中的浸入曲面. S在M中的Kahler角是由Chern和Wolfson [Am. 105（1983）59-83]。令（M，（g）over bar（t））沿着Kahler-Ricci流演化，Sigma t in（M，（g）over bar（t）沿着平均曲率流演化。我们证明了Kahler角α（t）满足演化方程（偏导数/偏导数（t）- Delta）cos α =|（del）跨棒J Sigma（t）|（2）cos alpha +Rsin（2）alpha cos alpha，其中R是（M，（g））在bar（t）上的标量曲率，该方程意味着如果初始曲面是辛曲面，（拉格朗日），那么，沿着流动，St总是辛的（拉格朗日）在每个时间t，我们称之为辛本文主要研究辛Kahler-Ricci平均曲率流。
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.