On the sectional curvature of compact hypersurfaces

Authors:
Leslie Coghlan and Yoe Itokawa

Journal:
Proc. Amer. Math. Soc. **109** (1990), 215-221

MSC:
Primary 53C40; Secondary 53C42

MathSciNet review:
1010797

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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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DOI:
https://doi.org/10.1090/S0002-9939-1990-1010797-1

Article copyright:
© Copyright 1990
American Mathematical Society