Actions of loop groups on simply connected H-surfaces in space forms

Atsushi FUJIOKA

doi:10.2969/jmsj/05040819

Atsushi FUJIOKA

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JOURNAL FREE ACCESS

1998 Volume 50 Issue 4 Pages 819-829

DOI https://doi.org/10.2969/jmsj/05040819

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Published: 1998 Received: November 28, 1995 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : [BG] M. J. Bergvelt and M. A. Guest, Actions of loop groups on harmonic maps, Trans. Amer. Math. Soc. 326 (1991), 861-886.
[BP] F. E. Burstall and F. Pedit, Dressing orbits of harmonic maps, Duke Math. J. 80 (1995), 353-382.
[DPW] J. Dorfmeister, F. Pedit and H. Wu, Weierstrass type representation of harmonic maps into symmetric spaces, preprint (1994).
[F] A. Fujioka, Harmonic maps and associated maps from simply connected Riemann surfaces into the 3-dimensional space forms, Tohoku Math. J. 47 (1995), 431-439.
[GO1] M. A. Guest and Y. Ohnita, Group actions and deformations for harmonic maps, J. Math. Soc. Japan 45 (1993), 671-704.
[GO2] M. A. Guest and Y. Ohnta, Loop group actions on harmonic maps and their applications, Harmonic Maps and Integrable Systems, A. Fordy and J. C. Wood, eds., Aspects of Mathematics E23 (1994), 273-292.
[Mc] I. McIntosh, Global solutions of the elliptic 2D periodic Toda lattice, Nonlinearity 7 (1994), 85-108.
[M] J. W. Milnor, Remarks on infinite dimensional Lie groups, in: Relativity, Groups and Topology II, B.S. de Witt, R. Stora (editors) (1984), North-Holland, Amsterdam.
[OMYK] H. Omori, Y. Maeda, A. Yoshioka and 0. Kobayashi, On Regular Fréchet-Lie Groups V, Tokyo J. Math. 6 (1983), 39-64.
[PS] A. N. Pressley and G. B. Segal, Loop groups, Oxford University Press, 1986.
[U] K. Uhlenbeck, Harmonic maps into Lie groups (Classical solutions of the chiral model), J. Differential Geom. 30 (1989), 1-50.

Right : [BG] M. J. Bergvelt and M. A. Guest, Actions of loop groups on harmonic maps, Trans. Amer. Math. Soc. 326 (1991), 861-886.
[BP] F. E. Burstall and F. Pedit, Dressing orbits of harmonic maps, Duke Math. J. 80 (1995), 353-382.
[DPW] J. Dorfmeister, F. Pedit and H. Wu, Weierstrass type representation of harmonic maps into symmetric spaces, preprint (1994).
[F] A. Fujioka, Harmonic maps and associated maps from simply connected Riemann surfaces into the 3-dimensional space forms, Tôhoku Math. J. 47 (1995), 431-439.
[GO1] M. A. Guest and Y. Ohnita, Group actions and deformations for harmonic maps, J. Math. Soc. Japan 45 (1993), 671-704.
[GO2] M. A. Guest and Y. Ohnita, Loop group actions on harmonic maps and their applications, Harmonic Maps and Integrable Systems, A. Fordy and J. C. Wood, eds., Aspects of Mathematics E23 (1994), 273-292.
[Mc] I. McIntosh, Global solutions of the elliptic 2D periodic Toda lattice, Nonlinearity 7 (1994), 85-108.
[M] J. W. Milnor, Remarks on infinite dimensional Lie groups, in: Relativity, Groups and Topology II, B. S. de Witt, R. Stora (editors) (1984), North-Holland, Amsterdam.
[OMYK] H. Omori, Y. Maeda, A. Yoshioka and O. Kobayashi, On Regular Fréchet-Lie Groups V, Tokyo J. Math. 6 (1983), 39-64.
[PS] A. N. Pressley and G. B. Segal, Loop groups, Oxford University Press, 1986.
[U] K. Uhlenbeck, Harmonic maps into Lie groups (Classical solutions of the chiral model), J. Differential Geom. 30 (1989), 1-50.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

Abstract

In this paper we shall define certain loop groups which act on simply connected H-surfaces in space forms preserving conformality, and obtain a criterion for these group actions to be equivariant.

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