复格拉斯曼流形G(2,5)中的调和2-球面

摘要

运用调和序列和活动标架研究复格拉斯曼流形G(2,5)中的调和2-球面.通过S2上全纯微分形式的构造,简化G(2,5)中沿调和2-球面的活动标架,并且给出高斯曲率的上界估计.%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).