AI 中文总结
研究欧几里得空间中严格凸超曲面与特定非负曲率空间乘积的标量曲率刚性，基于弗雷德霍姆族指标定理给出证明，恢复了相关结果。
AI 中文摘要
我们按照Llarull以及Goette - Semmelmann的思路，给出了欧几里得空间中严格凸超曲面与具有非零欧拉特征的非负曲率空间乘积的标量曲率刚性的证明。我们的证明基于弗雷德霍姆族指标定理，恢复了Lockman - Zeidler使用克利福德线性（族）指标理论得到的相应结果。
英文摘要
We give a proof of scalar curvature rigidity in the spirit of Llarull and Goette-Semmelmann for products of strictly convex hypersurfaces in Euclidean space and nonnegatively curved spaces with non-vanishing Euler-characteristic. Our proof is based on the Fredholm family index theorem. This recovers corresponding results of Lockman-Zeidler where Clifford-linear (family) index theory is used.
Comments10 pages, 1 figure;
