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Durham University

Department of Mathematical Sciences

Staff

Publication details for Dr John Bolton

Bolton, John. & Woodward, L. M. (2003). Toda equations and Plücker formulae. Bulletin of the London Mathematical Society 35(2): 145-151.

Author(s) from Durham

Abstract

An extension is obtained to certain maps into full flag manifolds of compact simple Lie groups of the classical Pluecker formulae for holomorphic curves in complex projectuive space.

References

1. M. Black, Harmonic maps into homogeneous spaces (Longman, 1991).
2. J. Bolton and L. M. Woodward, `Minimal surfaces and the Toda equations for the classical groups',
Geometry and topology of submanifolds VIII (World Scienti c, 1996) 22{30.
3. J. Bolton and L. M. Woodward, `Some geometrical aspects of the 2-dimensional Toda equations',
Geometry, topology and physics, Proceedings of the First Brazil-USA Workshop, Campinas,
Brazil, 1996 (ed. B. N. Apanasov et al., de Gruyter, 1997) 69{81.
4. J. Bolton, G. R. Jensen, M. Rigoli and L. M. Woodward, `On conformal minimal immersions of
S2 into CPn', Math. Ann. 279 (1988) 599{620.
5. J. Bolton, F. Pedit and L. M. Woodward, `Minimal surfaces and the ane Toda eld model',
J. Reine Angew. Math. 459 (1995) 119{150.
6. F. E. Burstall and F. Pedit, `Harmonic maps via Adler{Kostant{Symes theory', Harmonic maps
and integrable systems (ed. A. P. Fordy and J. C. Wood, Vieweg, 1993) 221{272.
7. F. E. Burstall and J. H. Rawnsley, Twistor theory for Riemannian symmetric spaces with applications
to harmonic maps of Riemann surfaces, Lecture Notes in Math. 1424 (Springer, Berlin, 1990).
8. A. P. Fordy, `Integrable equations associated with simple Lie algebras and symmetric spaces', Soliton
theory: a survey of results (ed. A. P. Fordy, Manchester Univ. Press, 1990) 315{337.
9. W. Fulton and J. Harris Representation theory (Springer, 1991).
10. P. Griffiths and J. Harris. Principles of algebraic geometry (Wiley-Interscience, 1974).
11. A. L. Onishchik and E. B. Vinberg, Lie groups and algebraic groups (Springer, 1990).
12. L. E. Positsel'skii, `Local Pl¨ucker formulas for a semisimple Lie group', Funct. Anal. Appl. 25 (1991)
291{292.
13. A. V. Razumov and M. V. Saveliev, `Di erential geometry of Toda systems', Comm. Anal. Geom.
461 (1994).
14. H. Samelson, Notes on Lie algebras (Springer, 1990).
15. J. A. Wolf, Spaces of constant curvature (Publish or Perish, 1974).

Notes

© Cambridge University Press 2003.