An estimate for the sectional curvature of cylindrically bounded submanifolds

2009/07/28 by Luis J. Alias, Luis J. Alı́as, G. Pacelli Bessa +5
Mathematics · #53C42 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #math.DG #msc:53C42

paper · pdf · doi:10.48550/arxiv.0907.5025

To appear in the Transactions of the American Mathematical Society

openalex publication_date 2009/07/28 · arxiv created 2011/09/29 · arxiv updated 2011/09/30 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

We give sharp sectional curvature estimates for complete immersed cylindrically bounded m-submanifolds ϕ:M→ N×ℝ^ℓ, 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 [7]

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