挤压子流形的几何与拓扑刚性
Geometric and topological rigidity of pinched submanifolds
浏览论文内容
中文总结 AI 辅助
针对空间形式中满足第二基本形式长度与平均曲率挤压条件的任意余维数紧致子流形，证明其要么使中间维度同调消失，要么确定子流形至全等，结果精确且无额外平均曲率假设地推广了前人成果。
中文摘要 AI 辅助
我们研究空间形式中任意余维数的紧致子流形的几何与拓扑，这些子流形满足涉及第二基本形式长度和平均曲率的特定挤压条件。我们证明，该挤压条件要么迫使中间维度范围内的同调消失，要么完全确定子流形直至全等。结果是精确的，且在不对平均曲率施加任何额外假设的情况下推广了多位作者的先前结果。
英文摘要
We investigate the geometry and topology of compact submanifolds of arbitrary codimension in space forms satisfying a certain pinching condition involving the length of the second fundamental form and the mean curvature. We prove that this pinching condition either forces homology to vanish in a range of intermediate dimensions, or completely determines the submanifold up to congruence. The results are sharp and extend previous results due to several authors without imposing any further assumption on the mean curvature.
