Harmonic tori in quaternionic projective 3-spaces
HTML articles powered by AMS MathViewer
- by Seiichi Udagawa PDF
- Proc. Amer. Math. Soc. 125 (1997), 275-285 Request permission
Abstract:
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 2- or 3-dimensional quaternionic projective space, which are not always covered by primitive harmonic two-tori of finite type.References
- Adel Bahy-El-Dien and John C. Wood, The explicit construction of all harmonic two-spheres in quaternionic projective spaces, Proc. London Math. Soc. (3) 62 (1991), no. 1, 202–224. MR 1078220, DOI 10.1112/plms/s3-62.1.202
- F. E. Burstall, Harmonic tori in spheres and complex projective spaces, preprint.
- F. E. Burstall, D. Ferus, F. Pedit, and U. Pinkall, Harmonic tori in symmetric spaces and commuting Hamiltonian systems on loop algebras, Ann. of Math. (2) 138 (1993), no. 1, 173–212. MR 1230929, DOI 10.2307/2946637
- J. Bolton, F. Pedit, and L. Woodward, Minimal surfaces and the affine Toda field model, J. Reine Angew. Math. (to appear).
- F. E. Burstall and F. Pedit, Harmonic maps via Adler-Kostant-Symes theory, Harmonic maps and Integrable Systems (A.P. Fordy and J.C. Wood, eds.), Aspects of Mathematics E23, Vieweg, 1994, pp. 221–272. CMP 94:09
- Francis E. Burstall and John H. Rawnsley, Twistor theory for Riemannian symmetric spaces, Lecture Notes in Mathematics, vol. 1424, Springer-Verlag, Berlin, 1990. With applications to harmonic maps of Riemann surfaces. MR 1059054, DOI 10.1007/BFb0095561
- F. E. Burstall and J. C. Wood, The construction of harmonic maps into complex Grassmannians, J. Differential Geom. 23 (1986), no. 3, 255–297. MR 852157
- D. Ferus, F. Pedit, U. Pinkall, and I. Sterling, Minimal tori in $S^4$, J. Reine Angew. Math. 429 (1992), 1–47. MR 1173114, DOI 10.1515/crll.1992.429.1
- James F. Glazebrook, The construction of a class of harmonic maps to quaternionic projective space, J. London Math. Soc. (2) 30 (1984), no. 1, 151–159. MR 760884, DOI 10.1112/jlms/s2-30.1.151
- N. J. Hitchin, Harmonic maps from a $2$-torus to the $3$-sphere, J. Differential Geom. 31 (1990), no. 3, 627–710. MR 1053342
- Oldřich Kowalski, Generalized symmetric spaces, Lecture Notes in Mathematics, vol. 805, Springer-Verlag, Berlin-New York, 1980. MR 579184
- S. Udagawa, Harmonic maps from a two-torus into a complex Grassmann manifold, International J. Math. 6 (1995), 447–459. CMP 95:11
- Jon G. Wolfson, Harmonic sequences and harmonic maps of surfaces into complex Grassmann manifolds, J. Differential Geom. 27 (1988), no. 1, 161–178. MR 918462
- John C. Wood, The explicit construction and parametrization of all harmonic maps from the two-sphere to a complex Grassmannian, J. Reine Angew. Math. 386 (1988), 1–31. MR 936991, DOI 10.1515/crll.1988.386.1
Additional Information
- Seiichi Udagawa
- Affiliation: Department of Mathematics, School of Medicine, Nihon University, Itabashi, Tokyo 173, Japan
- Email: h01217@sinet.ad.jp
- Received by editor(s): June 26, 1995
- Communicated by: Peter Li
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 275-285
- MSC (1991): Primary 58E20, 53C42
- DOI: https://doi.org/10.1090/S0002-9939-97-03638-1
- MathSciNet review: 1353402