A sphere theorem for odd-dimensional submanifolds of spheres

Vlachos, Theodoros

doi:10.1090/S0002-9939-01-06096-8

A sphere theorem for odd-dimensional submanifolds of spheres
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Proc. Amer. Math. Soc. 130 (2002), 167-173 Request permission

Abstract:

We establish a topological sphere theorem from the point of view of submanifold geometry for odd-dimensional submanifolds $M^n$ of a unit sphere. We give examples which show that our result is optimal. Moreover, we note the assumption that the dimension $n$ is odd is essential.

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