## 8 Citations

New constructions of twistor lifts for harmonic maps

- Mathematics
- 2011

We show that given a harmonic map φ from a Riemann surface to a classical compact simply connected inner symmetric space, there is a J2-holomorphic twistor lift of φ (or its negative) if and only if…

Harmonic surfaces in the Cayley plane

- MathematicsJournal of the London Mathematical Society
- 2020

We consider the twistor theory of nilconformal harmonic maps from a Riemann surface into the Cayley plane OP2=F4/Spin(9) . By exhibiting this symmetric space as a submanifold of the Grassmannian of…

Harmonic maps and shift-invariant subspaces

- Mathematics
- 2018

We investigate in detail the connection between harmonic maps from Riemann surfaces into the unitary group $\U(n)$ and their Grassmannian models which are families of shift-invariant subspaces of…

Harmonic maps into the exceptional symmetric space G2/SO(4)

- MathematicsJ. Lond. Math. Soc.
- 2015

We show that a harmonic map from a Riemann surface into the exceptional symmetric space G2/ SO (4) has a J2 ‐holomorphic twistor lift into one of the three flag manifolds of G2 if and only if it is…

Filtrations, Factorizations and Explicit Formulae for Harmonic Maps

- Mathematics
- 2009

We use filtrations of the Grassmannian model to produce explicit algebraic formulae for all harmonic maps of finite uniton number from a Riemann surface, and so all harmonic maps from the 2-sphere,…

Symmetric shift-invariant subspaces and harmonic maps

- MathematicsMathematische Zeitschrift
- 2021

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant…

FA ] 4 D ec 2 01 9 SYMMETRIC SHIFT-INVARIANT SUBSPACES AND HARMONIC MAPS

- Mathematics
- 2019

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant…

Diagrams and harmonic maps, revisited

- Mathematics
- 2022

. We extend many known results for harmonic maps from the 2-sphere into a Grassmannian to harmonic maps of ﬁnite uniton number from an arbitrary Riemann surface. Our method relies on a new theory of…

## References

SHOWING 1-10 OF 18 REFERENCES

Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras

- Mathematics
- 1993

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

- Mathematics
- 1996

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

- Mathematics
- 1997

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

- Mathematics
- 1998

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

- MathematicsInt. J. Math. Math. Sci.
- 2005

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

- Mathematics
- 1986

(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

- Mathematics
- 2007

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.

- Mathematics
- 1988

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

- Mathematics
- 1991

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…