An estimate for the sectional curvature of cylindrically bounded submanifolds

Abstract

We give sharp sectional curvature estimates for complete immersed cylindrically bounded $m$-submanifolds $\varphi :M\to N\times {\mathbb{R}}^{\ell }$, $n+\ell \le 2m-1$ provided that either $\varphi$ 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]

To appear in the Transactions of the American Mathematical Society

References in corpus (1)

• The mean curvature of cylindrically bounded submanifolds