论文标题
在有限的对称域中的完全测量盘
Totally geodesic discs in bounded symmetric domains
论文作者
论文摘要
在本文中，我们表征了$ c^2 $ -Smooth完全地理等轴测嵌入$ f \ colonω\toΩ$ tomome $之间，有界对称域$ω$和$ω'$，它们扩展了$ c^1 $ -smooth，在Shilov Bundaries的某些开放子集中，Shilov Bundaries中的某些开放子集和具有非试点的正常派生范围。特别是，如果$ω$不可修复，则完全存在完全地理界的对称子域$ω_1$和$ω_________________________________________________________________________________________________________2等距嵌入。如果$ \ text {rank}（ω'）<2 \ text {rank}（ω）$，则$ f $或$ \ bar f $是标准的holomorphic嵌入。
In this paper, we characterize $C^2$-smooth totally geodesic isometric embeddings $f\colon Ω\toΩ'$ between bounded symmetric domains $Ω$ and $Ω'$ which extend $C^1$-smoothly over some open subset in the Shilov boundaries and have nontrivial normal derivatives on it. In particular, if $Ω$ is irreducible, there exist totally geodesic bounded symmetric subdomains $Ω_1$ and $Ω_2$ of $Ω'$ such that $f = (f_1, f_2)$ maps into $Ω_1\times Ω_2\subset Ω$ where $f_1$ is holomorphic and $f_2$ is anti-holomorphic totally geodesic isometric embeddings. If $\text{rank}(Ω')<2\text{rank}(Ω)$, then either $f$ or $\bar f$ is a standard holomorphic embedding.
