On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds
Archivum Mathematicum (2005)
- Volume: 041, Issue: 3, page 273-280
- ISSN: 0044-8753
Access Full Article
topAbstract
topHow to cite
topYe, Bing Wu. "On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds." Archivum Mathematicum 041.3 (2005): 273-280. <http://eudml.org/doc/249495>.
@article{Ye2005,
abstract = {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.},
author = {Ye, Bing Wu},
journal = {Archivum Mathematicum},
keywords = {complex Grassmann manifold; harmonic map; harmonic sequence; genus; the generalized Frenet formulae; harmonic map; harmonic sequence; genus; generalized Frenet formulae},
language = {eng},
number = {3},
pages = {273-280},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds},
url = {http://eudml.org/doc/249495},
volume = {041},
year = {2005},
}
TY - JOUR
AU - Ye, Bing Wu
TI - On the degeneration of harmonic sequences from surfaces into complex Grassmann manifolds
JO - Archivum Mathematicum
PY - 2005
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 041
IS - 3
SP - 273
EP - 280
AB - 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.
LA - eng
KW - complex Grassmann manifold; harmonic map; harmonic sequence; genus; the generalized Frenet formulae; harmonic map; harmonic sequence; genus; generalized Frenet formulae
UR - http://eudml.org/doc/249495
ER -
References
top- Chern S. S., Wolfson J. G., Harmonic maps of the two-spheres into a complex Grassmann manifold II, Ann. Math. 125 (1987), 301–335. (1987) MR0881271
- Wolfson J. G., Harmonic sequences and harmonic maps of surfaces into complex Grassmann manifolds, J. Diff. Geom. 27 (1988), 161–178. (1988) MR0918462
- Liao R., Cyclic properties of the harmonic sequence of surfaces in CP, Math. Ann. 296 (1993), 363–384. (1993) MR1219907
- Dong Y. X., On the isotropy of harmonic maps from surfaces to complex projective spaces, Inter. J. Math. 3 (1992), 165–177. (1992) Zbl0759.58013MR1146809
- Jensen G. R., Rigoli M., On the isotropy of compact minimal surfaces in CP, Math. Z. 200 (1989), 169–180. (1989) MR0978292
- Burstall F. E., Wood J. C., The construction of harmonic maps into complex Grassmannian, J. Diff. Geom. 23 (1986), 255–297. (1986) MR0852157
- Uhlenbeck K., Harmonic maps into Lie groups (classical solutions of the chiral model, J. Diff. Geom. 30 (1989), 1–50. (1989) Zbl0677.58020MR1001271
- Shen Y. B., Dong Y. X., On pseudo-holomorphic curves in complex Grassmannian, Chin. Ann. Math. 20B (1999), 341–350. (1999) MR1749475
- Eschenburg J. H., Guadalupe I. V., Tribuzy R. A., The fundamental equations of minimal surfaces in CP, Math. Ann. 270 (1985), 571–598. (1985) MR0776173
- Eells J., Wood J. C., Harmonic maps from surfaces to complex projective spaces, Adv. Math. 49 (1983), 217–263. (1983) Zbl0528.58007MR0716372
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.