Blasts from the past

1. F.E. Burstall, D. Ferus, F. Pedit, U. Pinkall Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras Ann. of Math. 138 (1993) 173-212 MR 94m:58057.

   We show how "most" harmonic 2-tori in a symmetric space are constructed from solutions of an algebraically completely integrable system.

   Reprints are available.

2. F. Burstall, S. Gutt, J. Rawnsley Twistor spaces for Riemannian symmetric spaces Math. Ann. 295 (1993) 729-743 MR 94f:53095.

   We describe the structure of the zero set of the Nijenhuis tensor of the twistor space of a non-inner Riemannian symmetric space.

   A few reprints are available as well as the preprint version as dvi, PostScript or pdf.

3. F. Burstall, O. Muskarov, G. Grantcharov, J. Rawnsley Hermitian structures on Hermitian symmetric spaces J. Geom. Phys. 10 (1993) 254-249 MR 94a:32051.

   The only (integrable) Hermitian structures on a Hermitian symmetric space are the invariant ones..

   A few reprints are available as well as the preprint version as dvi, PostScript or pdf.

4. Harmonic tori in Lie groups in Geometry and topology of submanifolds, III (L. Verstraelen and A. West, eds) World Scientific 1991, pages 73-80 MR 96h:58042.

   First steps towards the story in the Annals paper: we write down an integrable pair of commuting Lax ODE on a loop algebra that produce harmonic maps.

   The preprint version is available as dvi, PostScript or pdf.

5. Harmonic maps and soliton theory Mat. Contemp. 2 (1992) 1-18 MR 96g:58042.

   An overview of the results in the Annals paper together with my only excursion into Algebraic Geometry: I use the beautiful formalism of Griffiths ( MR 87c:58048) to show that the Lax equations linearise on the Jacobian of the spectral curve.

   The preprint version is available as dvi, PostScript or pdf.

6. Minimal surfaces in quaternionic symmetric spaces in Geometry of Low-Dimensional Manifolds, 1 (S.K. Donaldson and C.B. Thomas, eds.) L.M.S. Lect. Notes vol. 150, Cambridge Univ. Press 1990, pages 231-235 MR 93i:53058.

   There is a birational contact transformation between the twistor spaces of any two Wolf spaces of the same dimension. This explains where the Bryant correspondence comes from. Later Kobak showed that these are the only possible examples amongst all flag manifolds ( MR 95e:32034).

   The preprint version is available as dvi, PostScript or pdf.

7. Riemannian twistor spaces and holonomy groups in Twistors in mathematics and physics (T.N. Bailey and R.J. Baston, eds.) L.M.S. Lect. Notes vol. 156, Cambridge Univ. Press 1990, pages 53-70 MR 92b:53110.

   Integrability of the canonical almost complex structure is examined on subbundles of twistor space picked out by the holonomy group.

   The preprint version is available as dvi, PostScript or pdf.