caa a22 4500 445835907 CHVBK 20180317145330.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00209-010-0675-8 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0675-8 Ng Sui-Chung Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China aut On holomorphic isometric embeddings of the unit n -ball into products of two unit m -balls [Elektronische Daten] [Sui-Chung Ng] 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 F 1(z)=(0, I n;m(z)) with the isometric constant equal to (m+1)/(n+1) and F 2(z)=(I n;m(z), I n;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. Springer-Verlag, 2010 Holomorphic isometric embeddings nationallicence Complex unit balls nationallicence Bergman metrics nationallicence Total geodesy nationallicence Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 347-354 0025-5874 268:1-2<347 2011 268 209 https://doi.org/10.1007/s00209-010-0675-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0675-8 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ng Sui-Chung Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 268/1-2(2011-06-01), 347-354 0025-5874 268:1-2<347 2011 268 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer