Hokkaido Mathematical Journal

Biharmonic maps into compact Lie groups and integrable systems

Hajime URAKAWA

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Abstract

In this paper, the formulation of the biharmonic map equation in terms of the Maurer-Cartan form for all smooth maps of a compact Riemannian manifold into a compact Lie group (G,h) with the bi-invariant Riemannian metric h is obtained. Using this, all biharmonic curves into compact Lie groups are determined exactly, and all the biharmonic maps of an open domain of ℝ2 equipped with a Riemannian metric conformal to the standard Euclidean metric into (G,h) are determined.

Article information

Source
Hokkaido Math. J., Volume 43, Number 1 (2014), 73-103.

Dates
First available in Project Euclid: 20 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1392906095

Digital Object Identifier
doi:10.14492/hokmj/1392906095

Mathematical Reviews number (MathSciNet)
MR3178481

Zentralblatt MATH identifier
1291.58007

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc.

Keywords
harmonic map biharmonic map compact Lie group integrable system Maurer-Cartan form

Citation

URAKAWA, Hajime. Biharmonic maps into compact Lie groups and integrable systems. Hokkaido Math. J. 43 (2014), no. 1, 73--103. doi:10.14492/hokmj/1392906095. https://projecteuclid.org/euclid.hokmj/1392906095


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