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- Title
Biharmonic Riemannian submersions from 3-manifolds.
- Authors
Wang, Ze-Ping; Ou, Ye-Lin
- Abstract
An important theorem about biharmonic submanifolds proved independently by Chen-Ishikawa (Kyushu J Math 52(1):167-185, 1998) and Jiang (Chin Ann Math Ser. 8A:376-383, 1987) 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, Caddeo et al. (Isr J Math 130:109-123, 2002) showed 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 into a surface is biharmonic if and only if it is harmonic.
- Subjects
SUBMANIFOLDS; BIHARMONIC functions; NUMERICAL solutions to biharmonic equations; RIEMANNIAN manifolds; HARMONIC functions
- Publication
Mathematische Zeitschrift, 2011, Vol 269, Issue 3/4, p917
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-010-0766-6