论文标题
有限的对称域之间完全测量的kobayashi等轴测图的全态性
Holomorphicity of totally geodesic Kobayashi isometry between bounded symmetric domains
论文作者
论文摘要
在本文中，我们研究了有限的对称域之间完全测量的kobayashi等距嵌入的全态性。首先，我们证明，对于$ c^1 $ -Smooth完全地理kobayashi等距嵌入$ f \ colonω\toΩ $ \ text {rank}（ω）\ geq \ text {rank}（f _*v）$对于任何切线向量$ v $ of $ω$，然后$ f $是holomorphicic or holomorphic or act tot holomorphic or act to holomorphic or as anti-lolomorphicic。其次，我们表征了$ c^1 $ kobayashi等法，从可还原有限的对称域到本身。
In this paper, we study the holomorphicity of totally geodesic Kobayashi isometric embeddings between bounded symmetric domains. First we show that for a $C^1$-smooth totally geodesic Kobayashi isometric embedding $f\colon Ω\toΩ'$ where $Ω$, $Ω'$ are bounded symmetric domains, if $Ω$ is irreducible and $\text{rank}(Ω) \geq \text{rank}(Ω')$ or more generally, $\text{rank}(Ω) \geq \text{rank}(f_*v)$ for any tangent vector $v$ of $Ω$, then $f$ is either holomorphic or anti-holomorphic. Secondly we characterize $C^1$ Kobayashi isometries from a reducible bounded symmetric domain to itself.
