Group actions and deformations for harmonic maps into symmetric spaces

Ohnita, Yoshihiro

doi:10.2996/kmj/1138040041

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Introduction and Statement Of Results2

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Cited by 3 publications

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“…The theory of harmonic maps into Lie groups, symmetric spaces or homogeneous spaces has been extensively studied related to the integrable systems by many authors (for instance, [14], [17], [3], [18], [9], [10], [11], [13], [2]). In particular, the moduli space of harmonic maps of 2-sphere into symmetric spaces was completely determined (cf.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

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Biharmonic maps into symmetric spaces and integrable systems

Urakawa¹

2011

Preprint

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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 R 2 with the standard Riemannian metric into (G/K, h) are characterized.2000 Mathematics Subject Classification. 58E20.

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Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…In particular, the moduli space of harmonic maps of 2-sphere into symmetric spaces was completely determined (cf. [3], [5], [13]). Let us recall the loop group formulation of harmonic maps into symmetric spaces, briefly.…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%