In this paper, we construct a class of homogeneous minimal 2-spheres in complex Grassmann manifolds by applying the irreducible unitary representations of SU （2）. Furthermore, we compute induced metrics, Gaussian cu...In this paper, we construct a class of homogeneous minimal 2-spheres in complex Grassmann manifolds by applying the irreducible unitary representations of SU （2）. Furthermore, we compute induced metrics, Gaussian curvatures, Khler angles and the square lengths of the second fundamental forms of these homogeneous minimal 2-spheres in G（2, n ＋ 1） by making use of Veronese sequence.展开更多
This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal sur...This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.展开更多
We study conformal minimal two-spheres immersed into the quaternionic projective spaceℍP^(n) by using the twistor map.We present a method to construct new minimal two-spheres with constant curvature inℍP^(n),based on ...We study conformal minimal two-spheres immersed into the quaternionic projective spaceℍP^(n) by using the twistor map.We present a method to construct new minimal two-spheres with constant curvature inℍP^(n),based on the minimal property and horizontal condition of Veronese map in complex projective space.Then we construct some concrete examples of conformal minimal two-spheres inℍP^(n) with constant curvature 2/n,n=4,5,6,respectively.Finally,we prove that there exist conformal minimal two-spheres with constant curvature 2/n inℍP^(n)(n≥7).展开更多
基金supported by the NSFC (11071248, 11071249)supported by the Fundamental Research Funds for the Central Universities(USTC)
文摘In this paper, we construct a class of homogeneous minimal 2-spheres in complex Grassmann manifolds by applying the irreducible unitary representations of SU （2）. Furthermore, we compute induced metrics, Gaussian curvatures, Khler angles and the square lengths of the second fundamental forms of these homogeneous minimal 2-spheres in G（2, n ＋ 1） by making use of Veronese sequence.
基金Supported by the National Natural Science Fundation of China.
文摘This paper deals with superminimal surfaces in complex space forms by using the Frenet framing. We formulate explicitly the length squares of the higher fundamental forms and the higher curvatures for superminimal surfaces in terms of the metric of the surface and the Khler angle of the immersion. Particularly, some curvature pinching theorems for minimal 2-spheres in a complex projective space are given and a new characterization of the Veronese sequence is obtained.
基金This work was supported in part by the National Natural Science Foundation of China(Grant No.11871450).
文摘We study conformal minimal two-spheres immersed into the quaternionic projective spaceℍP^(n) by using the twistor map.We present a method to construct new minimal two-spheres with constant curvature inℍP^(n),based on the minimal property and horizontal condition of Veronese map in complex projective space.Then we construct some concrete examples of conformal minimal two-spheres inℍP^(n) with constant curvature 2/n,n=4,5,6,respectively.Finally,we prove that there exist conformal minimal two-spheres with constant curvature 2/n inℍP^(n)(n≥7).
