$Q_6$中可约常曲率共形极小二维球面

Reducible Conformal Minimal Immersions with Constant Curvature from $S^2$ to $Q_6$

中文关键词:  共形极小浸入  常曲率  迷向阶  第二基本形式

英文关键词:conformal minimal immersion  constant curvature  isotropy order  second fundamental form

中文摘要:

      利用调和序列理论,我们研究了$Q_6$中共形极小二维球面的几何,给出了一定条件下从$S^2$到$Q_6$ (或者实Grassmann流形$G(2,8,{\mathbb{R}})$)中的线性满的可约常曲率共形极小浸入分类,同时在SO(8)-等价意义下,针对每种分类情形构造了非共轭的具体例子.

英文摘要:

      Using the harmonic map theory, we study the geometry of conformal minimal two-spheres immersed in $Q_6$, or a real Grassmannian manifold $G(2,8;\mr)$ equivalently. Then we classify the linearly full reducible conformal minimal immersions with constant Gaussian curvature from $S^2$ to $Q_6$ under some conditions. We also construct specific examples of non-congruent two-spheres with the same Gaussian curvature, up to $SO(8)$-equivalence, for each case.