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Geometriae Dedicata

, Volume 163, Issue 1, pp 379–390 | Cite as

Immersed surfaces in Lie algebras associated to primitive harmonic maps

  • R. Pacheco
Original Paper

Abstract

Sym and Bobenko gave a construction to recover a constant mean curvature surface in 3-dimensional euclidean space from the one-parameter family of harmonic maps associated to its Gauss map into the sphere. More recently, Eschenburg and Quast generalized this construction by replacing the sphere by a Kähler symmetric space of compact type. In this paper we shall take the generalization of Eschenburg and Quast a step further: our target space is now a generalized flag manifold N = G/K and we consider immersions of M in the Lie algebra \({\mathfrak{g}}\) of G associated to primitive harmonic maps.

Keywords

Primitive harmonic maps Generalized flag manifolds Immersed surfaces 

Mathematics Subject Classification (2000)

58E20 53C43 53C35 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade da Beira InteriorCovilhãPortugal

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