Euler characters and submanifolds of constant positive curvature

Moore, John

doi:10.1090/S0002-9947-02-03043-X

Euler characters and submanifolds of constant positive curvature
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Trans. Amer. Math. Soc. 354 (2002), 3815-3834 Request permission

Abstract:

This article develops methods for studying the topology of submanifolds of constant positive curvature in Euclidean space. It proves that if $M^n$ is an $n$-dimensional compact connected Riemannian submanifold of constant positive curvature in ${\mathbb E}^{2n-1}$, then $M^n$ must be simply connected. It also gives a conformal version of this theorem.

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