Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58E20, 53C42
  • Retrieve articles in all journals with MSC (1991): 58E20, 53C42
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