New results toward the classification of Biharmonic submanifolds in \mathbbSⁿ

2011/11/25 by A. Balmus, Balmus, A., Stefano Montaldo +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1111.6063

openalex publication_date 2011/11/25 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We prove some new rigidity results for proper biharmonic immersions in \mathbb Sⁿ of the following types: Dupin hypersurfaces; hypersurfaces, both compact and non-compact, with bounded norm of the second fundamental form; hypersurfaces satisfying intrinsic properties; PMC submanifolds; parallel submanifolds.

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