AI 中文总结
本文针对相同符号Levi非退化超曲面间全纯映射的霍普夫型性质猜想给出一般情形反例，并证明目标超曲面为任意余维超二次曲面时该猜想成立。
AI 中文摘要
二十多年前，Baouendi与第一作者证明，相同符号的超二次曲面之间的全纯映射要么完全退化，要么其法分量的法导数非零，这在无伪凸性的任意余维下建立了经典霍普夫引理的CR类比，他们还猜想，相同符号的Levi非退化超曲面之间的全纯映射也具有相同的霍普夫型性质。本文针对该猜想的一般情形给出了一个反例，同时证明当目标超曲面为任意余维的超二次曲面时该猜想成立，这可说是应用中最重要的情形。
英文摘要
More than twenty years ago, Baouendi and the first author proved that a holomorphic map between hyperquadrics of the same signature is either totally degenerate or has a nonvanishing normal derivative for its normal component. This established a CR analogue of the classical Hopf lemma in arbitrary codimension, in the absence of pseudoconvexity. They further conjectured that the same Hopf-type property holds for holomorphic maps between Levi-nondegenerate hypersurfaces of the same signature. In this paper, we provide a counterexample to this conjecture in full generality. We also prove the conjecture when the target hypersurface is a hyperquadric of any codimension, arguably the most important case for applications.
