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Article overview
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Biharmonic Riemannian submersions from 3-manifolds | Ze-Ping Wang
; Ye-Lin Ou
; | Date: |
24 Feb 2010 | Abstract: | An 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 | Services: | Forum | Review | PDF | Favorites |
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