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arXiv · 0907.5025

An estimate for the sectional curvature of cylindrically bounded submanifolds

Luis J. Alias·G. Pacelli Bessa·J. Fabio Montenegro
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Abstract

We give sharp sectional curvature estimates for complete immersed cylindrically bounded $m$-submanifolds $\phi:M\to N\times\mathbb{R}^{\ell}$, $n+\ell\leq 2m-1$ provided that either $\phi$ is proper with the second fundamental form with certain controlled growth or $M$ has scalar curvature with strong quadratic decay. This latter gives a non-trivial extension of the Jorge-Koutrofiotis Theorem [7]

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Luis J. Alias, G. Pacelli Bessa, J. Fabio Montenegro. 2009-07-28. An estimate for the sectional curvature of cylindrically bounded submanifolds. https://arxiv.org/abs/0907.5025

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