caa a22 4500 445836652 CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0766-6 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0766-6 Biharmonic Riemannian submersions from 3-manifolds [Elektronische Daten] [Ze-Ping Wang, Ye-Lin Ou] 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 etal. (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. Springer-Verlag, 2010 Biharmonic maps nationallicence Riemannian submersions nationallicence Harmonic morphisms nationallicence 3-manifolds nationallicence Wang Ze-Ping Department of Mathematics and Physics, Yunnan Wenshan University, No. 2, Xuefu Road, Wenshan County, 653000, Wenshan, Yunnan, People's Republic of China aut Ou Ye-Lin Department of Mathematics, Texas A & M University-Commerce, 75429, Commerce, TX, USA aut Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 917-925 0025-5874 269:3-4<917 2011 269 209 https://doi.org/10.1007/s00209-010-0766-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0766-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Ze-Ping Department of Mathematics and Physics, Yunnan Wenshan University, No. 2, Xuefu Road, Wenshan County, 653000, Wenshan, Yunnan, People's Republic of China aut NATIONALLICENCE 700 1- Ou Ye-Lin Department of Mathematics, Texas A & M University-Commerce, 75429, Commerce, TX, USA aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 917-925 0025-5874 269:3-4<917 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer