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An estimate for the sectional curvature of cylindricalli bounded submanifolds

We give sharp sectional curvature estimates for complete immersed cylindrically bounded m-submanifolds φ : M → N × Rl, n+ l ≤ 2m− 1 provided that either φ 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 [8]. Mathematics Subject Classification (2000): 53C42