Let $f:M\rightarrow G(m,n)$ be a harmonic map from surface into complex Grassmann manifold. In this paper, some sufficient conditions for the harmonic sequence generated by $f$ to have degenerate $\partial ^{\prime }$-transform or $\partial ^{\prime \prime }$-transform are given.
@article{107958, author = {Bing Wu Ye}, title = {On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds}, journal = {Archivum Mathematicum}, volume = {041}, year = {2005}, pages = {273-280}, zbl = {1114.53058}, mrnumber = {2188383}, language = {en}, url = {http://dml.mathdoc.fr/item/107958} }
Ye, Bing Wu. On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds. Archivum Mathematicum, Tome 041 (2005) pp. 273-280. http://gdmltest.u-ga.fr/item/107958/
Harmonic maps of the two-spheres into a complex Grassmann manifold II, Ann. Math. 125 (1987), 301–335. (1987) | MR 0881271
Harmonic sequences and harmonic maps of surfaces into complex Grassmann manifolds, J. Diff. Geom. 27 (1988), 161–178. (1988) | MR 0918462
Cyclic properties of the harmonic sequence of surfaces in CP$^{n}$, Math. Ann. 296 (1993), 363–384. (1993) | MR 1219907
On the isotropy of harmonic maps from surfaces to complex projective spaces, Inter. J. Math. 3 (1992), 165–177. (1992) | MR 1146809 | Zbl 0759.58013
On the isotropy of compact minimal surfaces in CP$^{n}$, Math. Z. 200 (1989), 169–180. (1989) | MR 0978292
The construction of harmonic maps into complex Grassmannian, J. Diff. Geom. 23 (1986), 255–297. (1986) | MR 0852157
Harmonic maps into Lie groups (classical solutions of the chiral model, J. Diff. Geom. 30 (1989), 1–50. (1989) | MR 1001271 | Zbl 0677.58020
On pseudo-holomorphic curves in complex Grassmannian, Chin. Ann. Math. 20B (1999), 341–350. (1999) | MR 1749475
The fundamental equations of minimal surfaces in CP$^{2}$, Math. Ann. 270 (1985), 571–598. (1985) | MR 0776173
Harmonic maps from surfaces to complex projective spaces, Adv. Math. 49 (1983), 217–263. (1983) | MR 0716372 | Zbl 0528.58007