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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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