Hokkaido Mathematical Journal

Biharmonic maps into symmetric spaces 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 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.

Article information

Source
Hokkaido Math. J., Volume 43, Number 1 (2014), 105-136.

Dates
First available in Project Euclid: 20 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1392906096

Digital Object Identifier
doi:10.14492/hokmj/1392906096

Mathematical Reviews number (MathSciNet)
MR3178482

Zentralblatt MATH identifier
1288.58008

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

Keywords
harmonic map biharmonic map symmetric space integrable system Maurer-Cartan form

Citation

URAKAWA, Hajime. Biharmonic maps into symmetric spaces and integrable systems. Hokkaido Math. J. 43 (2014), no. 1, 105--136. doi:10.14492/hokmj/1392906096. https://projecteuclid.org/euclid.hokmj/1392906096


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