On harmonic tori in compact rank one symmetric spaces

@article{Pacheco2009OnHT,
  title={On harmonic tori in compact rank one symmetric spaces},
  author={Rui Pacheco},
  journal={Differential Geometry and Its Applications},
  year={2009},
  volume={27},
  pages={352-361}
}
  • R. Pacheco
  • Published 1 June 2009
  • Mathematics
  • Differential Geometry and Its Applications
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References

SHOWING 1-10 OF 18 REFERENCES
Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras
Much of the qualitative behaviour of the problem can be seen in embryo form in the simplest possible case: that of harmonic maps of a compact Riemann surface M into S. If M is the Riemann sphere, all
Harmonic two-spheres in compact symmetric spaces, revisited
Uhlenbeck introduced an invariant, the (minimal) uniton number, of harmonic 2-spheres in a Lie group G and proved that when G=SU(n) the uniton number cannot exceed n-1. In this paper, using new
Harmonic tori in quaternionic projective 3-spaces
Burstall classified conformal non-superminimal harmonic two-tori in spheres and complex projective spaces. In this paper, we shall classify conformal non-superminimal harmonic two-tori in a 2or
Weierstrass type representation of harmonic maps into symmetric spaces
Over the past five years substantial progress has been made in the understanding of harmonic maps /: M —> G/K of a compact Riemann surface M into a compact symmetric space G/K [29, 30, 12, 14, 17,
Twistor fibrations giving primitive harmonic maps of finite type
  • R. Pacheco
  • Mathematics
    Int. J. Math. Math. Sci.
  • 2005
TLDR
This work will clarify and generalize Ohnita and Udagawa's results concerning homogeneous projections p:G/H→G/K, with H⊂K, preserving finite-type property for primitive harmonic maps.
A twistor description of harmonic maps of a 2-sphere into a Grassmannian
(0.3) Example. Let N be even-dimensional and orientable and ~ : J ( N ) ~ N be the fibre bundle whose fibre at x is the space of almost complex structures of TxN compatible with the orientation.
Adding a uniton via the DPW method
In this paper we describe how the operation of adding a uniton arises via the DPW method of obtaining harmonic maps into compact Riemannian symmetric spaces out of certain holomorphic one forms. We
The explicit construction and parametrization of all harmonic maps from the two-sphere to a complex Grassmannian.
A. Background. The construction and classification of all harmonic maps from the two-sphere (equivalently, minimal branched immersions) and certain harmonic maps from other Riemann surfaces to a
The Explicit Construction of All Harmonic Two‐Spheres in Quaternionic Projective Spaces
We show how to construct explicitly all harmonic maps (or, equivalently, branched minimal immersions) from the two-sphere to a quaternionic projective space. This forms part of a programme to
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