On the sectional curvature of compact hypersurfaces

Coghlan, Leslie; Itokawa, Yoe

doi:10.1090/S0002-9939-1990-1010797-1

On the sectional curvature of compact hypersurfaces
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by Leslie Coghlan and Yoe Itokawa PDF

Proc. Amer. Math. Soc. 109 (1990), 215-221 Request permission

Abstract:

We establish a sufficient condition for compact hypersurfaces of a complete riemannian manifold to be spherical. It is well known, from the works of Jacobowitz, Jorge and Koutroufiotis, and others, that the maximum sectional curvature of such hypersurfaces can be estimated from the curvature of the ambient space and the outer radius. Our result sharpens these estimates. It also implies a new nonimmersibility theorem of the Chern-Kuiper type.

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