Bochner-Simons formulas and the rigidity of biharmonic submanifolds

2018/01/24 by Fetcu, Dorel, Loubeau, Eric, Oniciuc, Cezar · 2 citations
#53C21 #53C24 #53C42 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.07879

Abstract

We find some integral formulas of Simons and Bochner type and use them to study biharmonic and biconservative submanifolds in space forms. We obtain rigidity results that in the biharmonic case represent partial answers to two well-known conjectures on such submanifolds in spheres.

Cited by

• Biconservative Weingarten surfaces with flat normal bundle in N⁴ (ε)
• Compact Biconservative Hypersurfaces in Space Forms: Rigidity Without Scalar Curvature Assumptions

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