论文标题
Clifford系统，谐波图和非负曲率的指标
Clifford systems, harmonic maps and metrics with non-negative curvature
论文作者
论文摘要
与对称的Clifford System $ \ {P_0，P_1，\ CDOTS，P_ {M} \} $相关联，$ \ Mathbb {r}^{2l} $，有一个规范矢量bundle $η$ hof $ s^{l-1} $。对于$ m = 4 $和$ 8 $，我们明确构建其特征图，并完全确定与$η$相关的Sphere Bunder bundle $ s（η）$接收横截面。这些将结果推广到\ cite {st51}和\ cite {ja58}中。作为一个应用程序，我们在同型球体组中建立了某些元素的新谐波代表（参见\ cite {pt97} \ cite {pt98}）。通过合适的Clifford系统选择，我们在$ s（η）$上构建了非负曲率的指标，这与ot-fkm类型的Isoparametric Hypersurfaces的不均匀焦点submanifold $ m _+$ m _+$ m _+$ m = 3 $。
Associated with a symmetric Clifford system $\{P_0, P_1,\cdots, P_{m}\}$ on $\mathbb{R}^{2l}$, there is a canonical vector bundle $η$ over $S^{l-1}$. For $m=4$ and $8$, we construct explicitly its characteristic map, and determine completely when the sphere bundle $S(η)$ associated to $η$ admits a cross-section. These generalize the results in \cite{St51} and \cite{Ja58}. As an application, we establish new harmonic representatives of certain elements in homotopy groups of spheres (cf. \cite{PT97} \cite{PT98}). By a suitable choice of Clifford system, we construct a metric of non-negative curvature on $S(η)$ which is diffeomorphic to the inhomogeneous focal submanifold $M_+$ of OT-FKM type isoparametric hypersurfaces with $m=3$.
