Journal of University of Chinese Academy of Sciences >
Harmonic two-spheres in the complex Grassmann manifold G(2,5)
Received date: 2010-10-18
Revised date: 2010-12-08
Online published: 2011-09-15
We use the methods of harmonic sequences and moving frames to study the harmonic two-spheres in the complex Grassmann manifold G(2,5). Through the construction of holomorphic differential forms on S2, we can simplify the moving frames along a harmonic two-sphere in G(2,5). Finally, we give some upper bounds of the Gauss curvature of minimal two-spheres in G(2,5).
LI Kang , JIAO Xiao-Xiang . Harmonic two-spheres in the complex Grassmann manifold G(2,5)[J]. Journal of University of Chinese Academy of Sciences, 2011 , 28(5) : 573 -582 . DOI: 10.7523/j.issn.2095-6134.2011.5.002
[1] Chern S S, Wolfson J G. Harmonic maps of the two-sphere into a complex Grassmann manifolds
[J]. Ann of Math, 1987, 125: 301-335.
[2] Chern S S, Wolfson J G. Minimal surfaces by moving frames
[J]. Amer J Math,1983, 105: 59-83.
[3] Wolfson J G. On minimal surfaces in a Kähler manifold of constant holomorphic sectional curvature
[J]. Trans Amer Math Soc, 1985, 290: 627- 646.
[4] Eschenburg J H, Guadalupe I V, Tribuzy R. The fundamental equation of minimal surfaces in CP2
[J]. Math Ann, 1985, 270: 571-598.
[5] Fei J, Jiao X X. Holomorphic 2-spheres in a complex complex Grassmann manifold G(2,5)
[J]. Journal of the Graduate University of the Chinese Academy of Sciences, 2011, 28(2): 131-140.
[6] Zheng Y. Quantization of curvature of harmonic two-spheres in Grassmann manifolds
[J]. Trans Amer Math Soc, 1989, 316: 193-214.
/
| 〈 |
|
〉 |