Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 62, Number 1 (2010), 55-73.
Biharmonic maps and morphisms from conformal mappings
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.
Tohoku Math. J. (2), Volume 62, Number 1 (2010), 55-73.
First available in Project Euclid: 31 March 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 58E20: Harmonic maps [See also 53C43], etc.
Secondary: 53C43: Differential geometric aspects of harmonic maps [See also 58E20]
Loubeau, Eric; Ou, Ye-Lin. Biharmonic maps and morphisms from conformal mappings. Tohoku Math. J. (2) 62 (2010), no. 1, 55--73. doi:10.2748/tmj/1270041027. https://projecteuclid.org/euclid.tmj/1270041027