The uniton numbers of the harmonic 2-spheres in Gr2(C4)

Hideko Sakagawa HASHIGUCHI

doi:10.2969/jmsj/04910081

The uniton numbers of the harmonic 2-spheres in Gr₂(C⁴)

Hideko Sakagawa HASHIGUCHI

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 1 Pages 81-105

DOI https://doi.org/10.2969/jmsj/04910081

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Published: 1997 Received: August 15, 1994 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 : Be-Gu) M. J. Bergvert and M. A. Guest, Actions of loop groups on harmonic maps, Trans. Amer. Math. Soc., 326 (1991), 861-886.
Bu-Sal) F. E. Burstall and S. M. Salamon, Tournaments, flags and harmonic maps, Math. Ann., 277 (1987), 247-265.
Bu-Woo) F. E. Burstall and J. C. Wood, The construction of harmonic maps into complex Grassmannians, J. Differential Geom., 23 (1986), 255-297.
C-Wol 1) S.-S. Chern and J. Wolfson, Harmonic maps of S² into a complex Grassman manifold, Proc. Natul. Acad. Sci. U.S. A., 82 (1985), 2217-2219.
C-Wol 2) S.-S. Chern and J. Wolfson, Harmonic maps of the two-sphere into a complex Grassmann manifold II, Ann. of Math., 125 (1987), 301-336.
D-Z 1) A. M. Din and W. J. Zakrzewski, General classical solutions in the CP^n-1 model, Nuclear Phys. B, 174 (1980), 397-406.
D-Z 2) A. M. Din and W. J. Zakrzewski, Properties of the general classical CP^n-1 model, Phys. Lett. B, 95 (1980), 419-422.
E-Woo) S. Erdem and J. C. Wood, On the construction of harmonic maps into Grassmannian, J. London Math. Soc., 28 (1983), 161-174.
Gl-St) V. Glaser and R. Stora, Regular solutions of the CPⁿ models and further generalizations, CERN, (1980), preprint.
K-M) J. L. Koszul and B. Malgrange, Sur certaines structures fibrées complexes, Arch. Math., 9 (1958), 102-109.
R) J. Ramanathan, Harmonic maps from S² to G_2,4, J. Differential Geom., 19, 207-219.
Sak) H. Sakagawa, On the extended solutions of isotropic harmonic 2-spheres into Grassmannian, Algebra Groups Geom., 11, 37-52.
Sal) S. Salamon, Harmonic and holomorphic maps, Geometry Seminar Luigi Bianchi II, Lecture Notes in Math., 1164, Springer, Berlin-Heidelberg-New York.
Sam) J. H. Sampson, Some properties and applications of harmonic mappings, Ann. Sci. École Norm. Sup., 11 (1978), 211-218.
U) K. Uhlenbeck, Harmonic maps into Lie groups (classical solutions of the chiral model), J. Differential Geom., 30 (1989), 1-50.

Right : [Be-Gu] M. J. Bergvert and M. A. Guest, Actions of loop groups on harmonic maps, Trans. Amer. Math. Soc., 326 (1991), 861-886.
[Bu-Sal] F. E. Burstall and S. M. Salamon, Tournaments, flags and harmonic maps, Math. Ann., 277 (1987), 247-265.
[Bu-Woo] F. E. Burstall and J. C. Wood, The construction of harmonic maps into complex Grassmannians, J. Differential Geom., 23 (1986), 255-297.
[C-Wol 1] S. -S. Chern and J. Wolfson, Harmonic maps of S² into a complex Grassman manifold, Proc. Natul. Acad. Sci. U. S. A., 82 (1985), 2217-2219.
[C-Wol 2] S. -S. Chern and J. Wolfson, Harmonic maps of the two-sphere into a complex Grassmann manifold II, Ann. of Math., 125 (1987), 301-336.
[D-Z 1] A. M. Din and W. J. Zakrzewski, General classical solutions in the CP^n-1 model, Nuclear Phys. B, 174 (1980), 397-406.
[D-Z 2] A. M. Din and W. J. Zakrzewski, Properties of the general classical CP^n-1 model, Phys. Lett. B, 95 (1980), 419-422.
[E-Woo] S. Erdem and J. C. Wood, On the construction of harmonic maps into Grassmannian, J. London Math. Soc., 28 (1983), 161-174.
[Gl-St] V. Glaser and R. Stora, Regular solutions of the CPⁿ models and further generalizations, CERN, (1980), preprint.
[K-M] J. L. Koszul and B. Malgrange, Sur certaines structures fibrées complexes, Arch. Math., 9 (1958), 102-109.
[R] J. Ramanathan, Harmonic maps from S² to G_2,4, J. Differential Geom., 19, 207-219.
[Sak] H. Sakagawa, On the extended solutions of isotropic harmonic 2-spheres into Grassmannian, Algebra Groups Geom., 11, 37-52.
[Sal] S. Salamon, Harmonic and holomorphic maps, Geometry Seminar Luigi Bianchi II, Lecture Notes in Math., 1164, Springer, Berlin-Heidelberg-New York.
[Sam] J. H. Sampson, Some properties and applications of harmonic mappings, Ann. Sci. École Norm. Sup., 11 (1978), 211-218.
[U] K. Uhlenbeck, Harmonic maps into Lie groups (classical solutions of the chiral model), J. Differential Geom., 30 (1989), 1-50.

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