Abstract
For a holomorphic proper map F from the ball \(\mathbb{B}^{n+1}\) into \(\mathbb{B}^{N+1}\) that is C 3 smooth up to the boundary, the image \(M=F(\partial\mathbb{B}^{n})\) is an immersed CR submanifold in the sphere \(\partial \mathbb{B}^{N+1}\) on which some second fundamental forms II M and \(\mathit{II}^{CR}_{M}\) can be defined. It is shown that when 4≤n+1<N+1≤4n−3, F is linear fractional if and only if \(\mathit{II}_{M} - \mathit{II}_{M}^{CR} \equiv 0\).
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Communicated by Alexander Isaev.
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Cheng, X., Ji, S. Linearity and Second Fundamental Forms for Proper Holomorphic Maps from \(\mathbb{B}^{n+1}\) to \(\mathbb{B}^{4n-3}\) . J Geom Anal 22, 977–1006 (2012). https://doi.org/10.1007/s12220-011-9225-9
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DOI: https://doi.org/10.1007/s12220-011-9225-9