Hokkaido Mathematical Journal

URAKAWA Hajime,

Biharmonic maps into symmetric spaces and integrable systems.

Hokkaido Mathematical Journal, 43 (2014) pp.105-136

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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 Riemannian symmetric space (G/K,h) induced from the bi-invariant Riemannian metric h on G is obtained. Using this, all the biharmonic curves into symmetric spaces are determined, and all the biharmonic maps of an open domain of ℝ2 with the standard Riemannian metric into (G/K,h) are characterized exactly.

MSC(Primary)58E20
MSC(Secondary)
Uncontrolled Keywordsharmonic map, biharmonic map, symmetric space, integrable system, Maurer-Cartan form