Hokkaido Mathematical Journal

URAKAWA Hajime,

Biharmonic maps into compact Lie groups and integrable systems.

Hokkaido Mathematical Journal, 43 (2014) pp.73-103

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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.

MSC(Primary)58E20
MSC(Secondary)
Uncontrolled Keywordsharmonic map, biharmonic map, compact Lie group, integrable system, Maurer-Cartan form