An estimate for the sectional curvature of cylindrically bounded submanifolds

Details An estimate for the sectional curvature of cylindrically bounded submanifolds An estimate for the sectional curvature of cylindrically bounded submanifolds

2009-07-28

arxiv.org/abs/0907.5025v3

Mathematics

Differential Geometry

To appear in the Transactions of the American Mathematical Society

Scientific paper

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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