Biharmonic maps into symmetric spaces and integrable systems

2011/01/17 by Urakawa, Hajime
#58E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1101.3152

Abstract

In this paper, the description of biharmonic map equation in terms of the Maurer-Cartan form for all smooth map 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. By this formula, all biharmonic curves into symmetric spaces are determined, and all the biharmonic maps of an open domain of \Bbb R² with the standard Riemannian metric into (G/K,h) are determined.

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