Tohoku Mathematical Journal

Classification of pluriharmonic maps from compact complex manifolds with positive first Chern class into complex Grassmann manifolds

Seiichi Udagawa

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 46, Number 3 (1994), 367-391.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178225718

Digital Object Identifier
doi:10.2748/tmj/1178225718

Mathematical Reviews number (MathSciNet)
MR1289185

Zentralblatt MATH identifier
0813.58012

Subjects
Primary: 58E20: Harmonic maps [See also 53C43], etc.
Secondary: 32H99: None of the above, but in this section

Citation

Udagawa, Seiichi. Classification of pluriharmonic maps from compact complex manifolds with positive first Chern class into complex Grassmann manifolds. Tohoku Math. J. (2) 46 (1994), no. 3, 367--391. doi:10.2748/tmj/1178225718. https://projecteuclid.org/euclid.tmj/1178225718


Export citation

References

  • [BD-Wl] A. BAHY-EL-DIEN AND J. C. WOOD, The explicit construction of all harmonic two-spheres in G2(Rn J. Reine Angew. Math. 398 (1989), 36-66.
  • [BD-W2] A. BAHY-EL-DIEN AND J. C. WOOD, The explicit construction of all harmonic two-spheres i quaternionic projective space, Proc. London Math. Soc. 62 (1991), 202-224.
  • [Bn] D. BURNS, Harmonic maps from CP1 to CP", Harmonic maps (Proceedings, New Orleans 1980, R. J. Knill, M. Kalka and H. C. J. Sealey, eds.), Lecture Notes in Math., 949 (1982), Springer-Verlag, Berlin, Heidelberg, New York, 48-56.
  • [B-B-B-R] D. BURNS, F. BURSTALL, P. DEBARTOLOMEIS AND J. RAWNSLEY, Stability of harmonic maps o Kahler manifolds, J. Differential Geom. 30 (1989), 579-594.
  • [B-B] D. BURNS AND P. DE BARTOLOMEIS, Applications harmoniques stables dans P", Ann. Sci. Ecol Norm. Sup. 21 (1988), 159-177.
  • [B-R] F. BURSTALL AND J. RAWNSLEY, Spheres harmoniques dans les groupes de Lie compacts e curbes holomorphes dans les espaces homogenes, C. R. Acad. Sc. Paris 302 (1986), 709-712.
  • [B-S] F. BURSTALL AND S. SALAMON, Tournaments, flags and harmonic maps, Math. Ann. 277 (1987), 249-265.
  • [B-W] F. BURSTALL AND J. C. WOOD, The construction of harmonic maps into complex Grassmannians, J. Differential Geom. 23 (1986), 255-297.
  • [C-T] J. A. CARLSON AND D. TOLEDO, Harmonic mappings of Kahler manifolds to locally symmetri spaces, Publication Math. Inst. Hautes. Etudes Sci. 69 (1990), 173-201.
  • [C-W] S. S. CHERN AND J. G. WOLFSON, Harmonic maps of the 2-sphere into a complex Grassman manifold, II, Ann. of Math. 125 (1987), 301-335.
  • [D-Z] A. M. DIN AND W. J. ZAKRZEWSKI, General classical solutions in the CP"'1 model, Nuclea Phys. B174 (1980), 397^06.
  • [E-L] J. EELLS AND L. LEMAIRE, Another report on harmonic maps, Bull. London Math. Soc. 2 (1988), 385-524.
  • [E-W] J. EELLS AND J. C. WOOD, Harmonic maps from surfaces to complex projective spaces, Adv Math. 49 (1983), 217-263.
  • [G-S] V. GLASER AND R. STORA, Regular solutions of the CP" models and further generalizations, preprint, 1980.
  • [O-U1] Y. OHNITA AND S. UDAGAWA, Stability, complex-analyticity and constancy of pluriharmoni maps from compact Kahler manifolds, Math. Z. 205 (1990), 629-644.
  • [O-U2] Y. OHNITA AND S. UDAGAWA, Complex-analyticity of pluriharmonic maps and thei constructions, (Proceedings, Katata/Kyoto 1989, J. Noguchi and T. Ohsawa, eds.), Lecture Notes in Math. 1468 (1991), Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 371^107.
  • [O-V] Y. OHNITA AND G. VALLI, Pluriharmonic maps into compact Lie groups and factorization int unitons, Proc. London Math. Soc. 61 (1990), 546-570.
  • [Rm] J. RAMANATHAN, Harmonic maps from S2 to G24, J. Differential Geom. 19 (1984), 207-219
  • [Ud] S. UDAGAWA, Holomorphy of certain stable harmonic maps and minimal immersions, Proc London Math. Soc. 57 (1988), 577-598.
  • [Uh] K. UHLENBECK, Harmonic maps into Lie groups (Classical solutions of the chiral model), J. Differential Geom. 30 (1989), 1-50.
  • [V] G. VALLI, On the energy spectrum of harmonic 2-spheres in unitary groups, Topology 27 (1988), 129-136.
  • [Wol] J. G. WOLFSON, Harmonic sequences and harmonic maps of surfaces into complex Grassman manifolds, J. Differential Geom. 27 (1988), 161-178.
  • [Wdl] J. C. WOOD, The explicit construction and parametrization of all harmonic maps from th two-sphere to a complex Grassmannians, J. Reine Angew. Math. 386 (1988), 1--31.
  • [Wd2] J. C. WOOD, Explicit construction and parametrization of harmonic two-spheres in the unitar group, Proc. London Math. Soc. 58 (1989), 608-624.