Linearity and Second Fundamental Forms for Proper Holomorphic Maps from \mathbb{B}^{n+1} to \mathbb{B}^{4n-3} |
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Authors: | Xiaoliang Cheng Shanyu Ji |
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Institution: | 1. Department of Mathematics, Capital Normal University, Beijing, 100048, China 2. Department of Mathematics, Jilin Normal University, Siping, 136000, China 3. Department of Mathematics, University of Houston, Houston, TX, 77204, USA
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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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