We use the Cartan embedding and the method of moving frame to study the geometry of 3-dimensional SU(2)-orbits in the complex Grassmann manifold G(k,n).
HAN Bing
,
WANG Jun
. Geometry of three-dimensional SU(2)-orbits in the complex Grassmannians[J]. Journal of University of Chinese Academy of Sciences, 2013
, 30(5)
: 585
-590
.
DOI: 10.7523/j.issn.2095-6134.2013.05.002
[1] Bando S, Ohnita Y. Minimal 2-spheres with constant curvature in CP [J]. J Math Soc Japan, 1987, 39(3): 477-487.
[2] Bolton J, Jensen G R, Rigoli M, et al. On conformal minimal immersions of S into CP [J]. Math Ann, 1988, 279: 599-620.
[3] Calabi E. Minimal immersions of surfaces in Euclidean spheres [J]. J Diff Geom, 1967, 1: 111-126.
[4] Carmo D, Wallach N R. Minimal immersions of spheres into spheres [J]. Ann Math, 1971, 93: 43-62.
[5] Eells J, Wood J C. Harmonic maps from surfaces to the complex projective spaces [J]. Adv Math, 1983, 49: 217-263.
[6] Fernandez L. The dimension and structure of the space of harmonic 2-spheres in the m-sphere [J]. Ann Math, 2012, 175: 1093-1125.
[7] Chern S S, Wolfson J G. Harmonic maps of the two-sphere into a complex Grassmann manifold II [J]. Ann Math, 1987, 125: 301-335.
[8] Uhlenbeck K. Harmonic maps into Lie groups [J]. J Diff Geom, 1989, 30: 1-50.
[9] Li Z Q, Wang C P, Wu F E. The classification of homogeneous 2-spheres in CP [J]. Asian J Math, 2001, 5(1): 93-108.
[10] Fei J, Jiao X X, Xiao L, et al. On the classification of homogeneous 2-spheres in the complex Grassmannians [J]. Osaka J Math, 2013, 50(1):135-152.
[11] Fei J, Peng C K, Xu X W. Equivariant totally real 3-spheres in the complex projective space CP [J]. Diff Geo App, 2012, 30:262-273.
[12] Mashimo. Minimal immersions of 3-dimensional sphere into spheres [J]. Osaka J Math, 1984, 21: 721-732.
[13] Li Z Q. Minimal S with constant curvature in CP [J]. J London Math Soc, 2003, 68(1): 223-240.
[14] Chen Q, Hu S, Xu X W. Construction of Lagrangian submanifolds in CP[J]. Pac J Math, 2012, 258(1): 31-49.
[15] Castro I, Li H Z, Urbano F. Hamiltonian-minimal Lagrangian submanifolds in complex space forms [J]. Pac Jour Math, 2006, 227(1): 43-63.
[16] Li Z Q, Tao Y Q. Equivariant Lagrangian minimal S in CP[J]. Act Math Sin, 2006, 22(4): 1215-1220.
