We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is diffeomorphic to a sphere or to a quotient of a sphere by a group action. We also prove another topological rigidity result for hypersurfaces of the sphere that involves the spherical image of its usual Gauss map.

中文翻译：

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椭圆空间形式封闭超曲面的拓扑刚性

我们证明了欧几里得球面和椭圆空间形式的封闭超曲面的拓扑刚性定理。它断言，在关于主曲率绝对值的下界假设下，超曲面与球体或通过群作用对球体的商微分同胚。我们还证明了球体超曲面的另一个拓扑刚性结果，其中涉及其通常的高斯图的球面图像。