On the Lagrangian angle and the Kahler angle of immersed surfaces in the complex plane C~2
On the Lagrangian angle and the Kahler angle of immersed surfaces in the complex plane C~2
复制标题
复平面C~2中浸入面的拉格朗日角和卡勒角
DOI：
10.1007/s10473-019-0617-4
复制
发表时间：
2019
影响因子：
1
通讯作者：
Li Xiao
中科院分区：
文献类型：
--
作者：
Li Xingxiao;Li Xiao
本文讨论了C~2中浸入曲面的Lagrange角和Kahler角。首先，我们将Lagrange角、Maslov形式和Maslov类推广到C~2中比Lagrange曲面更一般的曲面，然后自然地推广了J. M. Morvan推广到常Kahler角曲面，并通过应用证明了具有常Kahler角的紧致自收缩曲面的Maslov类一般是非零的。其次，我们得到了关于Kahler角的两个Pinching结果，这两个结果包含了具有Kahler角的自收缩体的刚性定理|H| ~2e-~（|X| ~2/2）dV_M < ∞，其中h和x分别表示曲面的第二基本形式和位置向量。
In this paper, we discuss the Lagrangian angle and the Kahler angle of immersed surfaces in C~2. Firstly, we provide an extension of Lagrangian angle, Maslov form and Maslov class to more general surfaces in C~2 than Lagrangian surfaces, and then naturally extend a theorem by J.-M. Morvan to surfaces of constant Kahler angle, together with an application showing that the Maslov class of a compact self-shrinker surface with constant Kahler angle is generally non-vanishing. Secondly, we obtain two pinching results for the Kahler angle which imply rigidity theorems of self-shrinkers with Kahler angle under the condition that ∫_M |h|~2e–~(|x|~2/2)dV_M < ∞, where h and x denote, respectively, the second fundamental form and the position vector of the surface.