Biharmonic submanifolds with parallel mean curvature in\n mathbbSⁿ\×\ℝ

2011/09/28 by Dorel Fetcu, Fetcu, Dorel, Cezar Oniciuc +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Biharmonic equation #Combinatorics #Constant (computer programming) #Curvature #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematics #Mean curvature #Product (mathematics) #Pure mathematics #Scalar curvature #Sectional curvature #Space (punctuation) #Space form #Submanifold #Type (biology) #math.DG

paper · pdf · doi:10.48550/arxiv.1109.6138

published in arXiv (Cornell University) (Cornell University) · 15 pages

arxiv created 2011/09/28 · openalex publication_date 2011/09/28 · arxiv updated 2011/09/29 · openalex created_date 2022/10/01 · openalex updated_date 2026/08/08

Abstract

We find a Simons type formula for submanifolds with parallel mean curvature\nvector (pmc submanifolds) in product spaces Mⁿ(c)\×\ℝ, where\nMⁿ(c) is a space form with constant sectional curvature c, and then we use\nit to prove a gap theorem for the mean curvature of certain complete\nproper-biharmonic pmc submanifolds, and classify proper-biharmonic pmc surfaces\nin mathbbSⁿ(c)\×\ℝ.\n

Citations

• Harmonic Mappings of Riemannian Manifolds
• Minimal Varieties in Riemannian Manifolds

Cited by

• Biharmonic hypersurfaces in a conformally flat space

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