In this paper, we study the holomorphicity of totally geodesic Kobayashi isometric embeddings between bounded symmetric domains. First, we show that for a -smooth totally geodesic Kobayashi isometric embedding where , are bounded symmetric domains, if is irreducible and or more generally, for any tangent vector of , then is either holomorphic or anti-holomorphic. Second, we characterize Kobayashi isometries from a reducible bounded symmetric domain to itself.

中文翻译：

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有界对称域间全测地小林等距的全纯性

在本文中，我们研究有界对称域之间完全测地小林等距嵌入的全纯性。首先，我们证明对于一个- 平滑完全测地小林等距嵌入在哪里,是有界对称域，如果是不可约的并且或者更一般地说，对于任意切向量的， 然后是全纯的或反全纯的。其次，我们表征小林从可约有界对称域到自身的等距。