A gap rigidity for proper holomorphic maps from $ \B^{n+1}$ to $ \B^{3n-1}$
| dc.creator | Wang, Seungho | |
| dc.date | 2006-04-18 | |
| dc.date.accessioned | 2026-07-07T07:11:00Z | |
| dc.date.available | 2026-07-07T07:11:00Z | |
| dc.description | Let $ \B^{n+1} \subset \C^{n+1}$ be the unit ball in a complex Euclidean space, and let $ Σ^n = \partial \B^{n+1} = S^{2n+1}$. Let $ f: Σ^n \hook Σ^{N}$ be a local CR immersion.If $ N-n<2n-1$, the asymptotic vectors of the second fundamental form of $ f$ at each point form a subspace of the holomorphic tangent space of $ Σ^n$ of codimension at most 1. We exploit the successive derivatives of this relation and show that a linearly full local CR immersion $ f: Σ^n \hook Σ^{N}$, $ N \leq 3n-2$, can only occur when $ N = n, 2n$, or $ 2n+1$. Together with the recent classification of the rational proper holomorphic maps from $ \B^{n+1}$ to $ \B^{2n+2}$ by Hamada, this gives a classification of the rational proper holomorphic maps from $ \B^{n+1}$ to $ \B^{3n-1}$ for $ n \geq 3$. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604382 | |
| dc.identifier | http://arxiv.org/abs/math/0604382 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111602 | |
| dc.subject | Differential Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 32H02 | |
| dc.title | A gap rigidity for proper holomorphic maps from $ \B^{n+1}$ to $ \B^{3n-1}$ | |
| dc.type | text |