论文标题
关于惠特尼球体的能源差距现象和相关问题
On energy gap phenomena of the Whitney sphere and related problems
论文作者
论文摘要
在本文中，我们研究了Lagrangian submanifolds满足$ {\ rm \ nabla^*} t = 0 $，Zhang \ cite \ cite {zh}在复杂空间的形式$ n（4c）中（c = 0 \ or \ \ 1）$ $ \ tilde {h} $是Lagrangian无跟踪的第二个基本形式。我们获得了一些Simons的类型积分不平等和此类Lagrangian Submanifolds的刚性定理。此外，我们在$ \ mathbb {c}^n $中研究Lagrangian submanifolds满足$ \ nabla^*\ nabla^*t = 0 $，并引入与它们相关的流程方法。
In this paper, we study Lagrangian submanifolds satisfying ${\rm \nabla^*} T=0$ introduced by Zhang \cite{Zh} in the complex space forms $N(4c)(c=0\ or \ 1)$, where $T ={\rm \nabla^*}\tilde{h}$ and $\tilde{h}$ is the Lagrangian trace-free second fundamental form. We obtain some Simons' type integral inequalities and rigidity theorems for such Lagrangian submanifolds. Moreover we study Lagrangian submanifolds in $\mathbb{C}^n$ satisfying $\nabla^*\nabla^*T=0$ and introduce a flow method related to them.
