Riemannian流形中受pinching条件约束的子流形的几何与拓扑刚性
Geometric and topological rigidity of pinched submanifolds in Riemannian manifolds
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中文总结 AI 辅助
研究Riemannian流形中满足第二基本形式范数与平均曲率的严格pinching条件的紧致子流形的刚性，揭示其几何与拓扑限制，扩展了球面定理等已知结果。
中文摘要 AI 辅助
我们研究满足严格pinching条件（涉及第二基本形式的范数和平均曲率）的Riemannian流形中任意余维数的紧致子流形的刚性。不假设 ambient 流形是空间形式，我们证明该条件对子流形施加了强烈的几何和拓扑限制。所得定理是尖锐的，并扩展了文献中几个已知结果，特别是球面定理，而无需额外假设。
英文摘要
We study the rigidity of compact submanifolds of Riemannian manifolds of arbitrary codimension that satisfy a sharp pinching condition involving the norm of the second fundamental form and the mean curvature. Without assuming that the ambient manifold is a space form, we show that this condition imposes strong geometric and topological restrictions on the submanifold. The resulting theorems are sharp and provide extensions of several known results in the literature, particularly sphere theorems, without requiring additional assumptions.
