| Title:
|
On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds (English) |
| Author:
|
Ye, Bing Wu |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
273-280 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
complex Grassmann manifold |
| Keyword:
|
harmonic map |
| Keyword:
|
harmonic sequence |
| Keyword:
|
genus |
| Keyword:
|
the generalized Frenet formulae |
| MSC:
|
53B30 |
| MSC:
|
53C42 |
| MSC:
|
53C43 |
| MSC:
|
58E20 |
| idZBL:
|
Zbl 1114.53058 |
| idMR:
|
MR2188383 |
| . |
| Date available:
|
2008-06-06T22:46:13Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107958 |
| . |
| Reference:
|
[1] Chern S. S., Wolfson J. G.: Harmonic maps of the two-spheres into a complex Grassmann manifold II.Ann. Math. 125 (1987), 301–335. MR 0881271 |
| Reference:
|
[2] Wolfson J. G.: Harmonic sequences and harmonic maps of surfaces into complex Grassmann manifolds.J. Diff. Geom. 27 (1988), 161–178. MR 0918462 |
| Reference:
|
[3] Liao R.: Cyclic properties of the harmonic sequence of surfaces in CP$^{n}$.Math. Ann. 296 (1993), 363–384. MR 1219907 |
| Reference:
|
[4] Dong Y. X.: On the isotropy of harmonic maps from surfaces to complex projective spaces.Inter. J. Math. 3 (1992), 165–177. Zbl 0759.58013, MR 1146809 |
| Reference:
|
[5] Jensen G. R., Rigoli M.: On the isotropy of compact minimal surfaces in CP$^{n}$.Math. Z. 200 (1989), 169–180. MR 0978292 |
| Reference:
|
[6] Burstall F. E., Wood J. C.: The construction of harmonic maps into complex Grassmannian.J. Diff. Geom. 23 (1986), 255–297. MR 0852157 |
| Reference:
|
[7] Uhlenbeck K.: Harmonic maps into Lie groups (classical solutions of the chiral model.J. Diff. Geom. 30 (1989), 1–50. Zbl 0677.58020, MR 1001271 |
| Reference:
|
[8] Shen Y. B., Dong Y. X.: On pseudo-holomorphic curves in complex Grassmannian.Chin. Ann. Math. 20B (1999), 341–350. MR 1749475 |
| Reference:
|
[9] Eschenburg J. H., Guadalupe I. V., Tribuzy R. A.: The fundamental equations of minimal surfaces in CP$^{2}$.Math. Ann. 270 (1985), 571–598. MR 0776173 |
| Reference:
|
[10] Eells J., Wood J. C.: Harmonic maps from surfaces to complex projective spaces.Adv. Math. 49 (1983), 217–263. Zbl 0528.58007, MR 0716372 |
| . |
