Biharmonic maps and morphisms from conformal mappings

• Loubeau Eric

  Departement de Mathematiques, Universite de Bretagne Occidentale

• Ou Ye-Lin

  Department of Mathematics, Texas A&M University-Commerce

Abstract

Inspired by the all-important conformal invariance of harmonic maps on two-dimensional domains, this article studies the relationship between biharmonicity and conformality. We first give a characterization of biharmonic morphisms, analogues of harmonic morphisms investigated by Fuglede and Ishihara, which, in particular, explicits the conditions required for a conformal map in dimension four to preserve biharmonicity and helps producing the first example of a biharmonic morphism which is not a special type of harmonic morphism. Then, we compute the bitension field of horizontally weakly conformal maps, which include conformal mappings. This leads to several examples of proper (i.e., non-harmonic) biharmonic conformal maps, in which dimension four plays a pivotal role. We also construct a family of Riemannian submersions which are proper biharmonic maps.

Journal

• Tohoku mathematical journal. Second series

  Tohoku mathematical journal. Second series 62 (1), 55-73, 2010-03

  Tohoku University

Details

• CRID: 1570291227599744000
• NII Article ID: 110007608285
• NII Book ID: AA00863953
• ISSN: 00408735
• Text Lang: en
• Data Source:
  • CiNii Articles