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An estimate of sectional curvatures of hypersurfaces with positive Ricci curvatures

Published online by Cambridge University Press:  20 January 2009

Ju Seon Kim  and
Sang Og Kim
Ju Seon Kim
Affiliation:
Department of MathematicsSeoul National University151–742, Korea
Sang Og Kim
Affiliation:
Department of MathematicsHallym University, 200–702, Korea
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Abstract

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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 1 , February 1995 , pp. 167 - 170
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Cheeger, J. and Ebin, D. G., Comparison theorems in Riemannian geometry (1975).Google Scholar
2.Jacobwitz, H., Isometric embedding of a compact Riemannian manifold into Euclidean space, Proc. Amer. Math. Soc. 40 (1973), 245–246.Google Scholar
3.Kobayashi, S. and Nomizu, K., Foundations of Differential Geometry (1969).Google Scholar