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Proceedings of the American Mathematical Society

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

 

 

Curvature estimates for complete and bounded submanifolds in a Riemannian manifold


Author: Yoshihisa Kitagawa
Journal: Proc. Amer. Math. Soc. 83 (1981), 579-581
MSC: Primary 53C20
DOI: https://doi.org/10.1090/S0002-9939-1981-0627696-1
MathSciNet review: 627696
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Abstract: Let $ M$ be a complete $ n$-dimensional submanifold in the $ (2n - 1)$-dimensional Euclidean space, with scalar curvature bounded from below. Baikousis and Koufogiorgos proved that the sectional curvature of $ M$ satisfies sup $ {K_M} \geqslant {\lambda ^{ - 2}}$ if $ M$ is contained in a ball of radius $ \lambda $. We extend this result to the case that the ambient space is a complete simply connected Riemannian manifold of nonpositive curvature.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627696-1
Article copyright: © Copyright 1981 American Mathematical Society