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Proceedings of the Edinburgh Mathematical Society
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Proceedings of the Edinburgh Mathematical Society
Article . 1995 . Peer-reviewed
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An estimate of sectional curvatures of hypersurfaces with positive Ricci curvatures

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Feb 1995 English Publisher:Cambridge University Press (CUP)Journal:Proceedings of the Edinburgh Mathematical Society, volume 38, pages 167-170 (issn: 0013-0915, eissn: 1464-3839, Copyright policy )
Authors: Ju Seon Kim; Sang Og Kim;

doi: 10.1017/s0013091500006283

An estimate of sectional curvatures of hypersurfaces with positive Ricci curvatures

Abstract

Let M be a hypersurface in Euclidean space and let the Ricci curvature of M be bounded below by some nonnegative constant. In this paper, we estimate the sectional curvature of M in terms of the lower bound of Ricci curvature and the upper bound of mean curvature.

Related Organizations
Keywords

positive Ricci curvature, hypersurfaces of Euclidean space, sectional curvature, Higher-dimensional and -codimensional surfaces in Euclidean and related \(n\)-spaces, Global Riemannian geometry, including pinching

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
bronze