On holomorphic isometric embeddings of the unit n-ball into products of two unit m-balls
On holomorphic isometric embeddings of the unit n-ball into products of two unit m-balls
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单位 n 球到两个单位 m 球乘积的全纯等距嵌入
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发表时间：
2011
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通讯作者：
Sui
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作者：
Sui
我们研究了复单位n-球关于两个复单位m-球关于其Bergman度量直到正规化常数(等距常数)的乘积的全纯等距嵌入。M≥n有两个平凡的全纯等距嵌入，其公式为：F1(Z)n=0(0，in；m(Z))，等距常数等于(m+1)/(n+1)；F2(Z)n=1(in；m(Z)，in；m(Z))，等距常数等于2(m+1)/(n+1).这里$${i_{n；m}：\mathbb{C}^n\Longright tarrow\mathbb{C}^m}$$是规范嵌入。我们证明了当m<；2n时，这是唯一的直到酉变换的全纯等距嵌入。
We study holomorphic isometric embeddings of the complex unit n-ball into products of two complex unit m-balls with respect to their Bergman metrics up to normalization constants (the isometric constant). There are two trivial holomorphic isometric embeddings for m ≥ n, given by F1(z) = (0, In;m(z)) with the isometric constant equal to (m + 1)/(n + 1) and F2(z) = (In;m(z), In;m(z)) with the isometric constant equal to 2(m + 1)/(n + 1). Here $${I_{n;m}:\mathbb{C}^n \longrightarrow \mathbb{C}^m}$$ is the canonical embedding. We prove that when m < 2n, these are the only holomorphic isometric embeddings up to unitary transformations.