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29 March 2024
 
  » arxiv » 1002.4439

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Biharmonic Riemannian submersions from 3-manifolds
Ze-Ping Wang ; Ye-Lin Ou ;
Date 24 Feb 2010
AbstractAn important theorem about biharmonic submanifolds proved independently by Chen-Ishikawa [CI] and Jiang [Ji] states that an isometric immersion of a surface into 3-dimensional Euclidean space is biharmonic if and only if it is harmonic (i.e, minimal). In a later paper [CMO2], Cadeo-Monttaldo-Oniciuc shown that the theorem remains true if the target Euclidean space is replaced by a 3-dimensional hyperbolic space form. In this paper, we prove the dual results for Riemannian submersions, i.e., a Riemannian submersion from a 3-dimensional space form of non-positive curvature into a surface is biharmonic if and only if it is harmonic.
Source arXiv, 1002.4439
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