Biharmonic and biconservative hypersurfaces in space forms

2020/12/23 by Fetcu, Dorel, Oniciuc, Cezar · 3 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.12476

Abstract

We present some general properties of biharmonic and biconservative submanifolds and then survey recent results on such hypersurfaces in space forms. We also propose an alternative version for a well-known result of Nomizu and Smyth for hypersurfaces by replacing the CMC hypothesis with the more general condition of biconservativity.

Cited by

• Classification of biharmonic Riemannian submersions from manifolds with constant sectional curvature
• Biconservative Weingarten surfaces with flat normal bundle in N⁴ (ε)
• Stable proper biharmonic maps in Euclidean spheres

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