论文标题
克利福德系统，克利福德结构及其规范差异形式
Clifford systems, Clifford structures, and their canonical differential forms
论文作者
论文摘要
Quaternionic $ 4 $ -form $φ_{sp（2）sp（1）} $的不同结构之间的比较与cayley校准$φ_{spin（7）} $的比较表明，一个人可以从相同的“Kähler2 forms”集合中启动。该比较与Clifford结构和Clifford系统的概念有关。 Going to dimension $16$, similar constructions allow to write explicit formulas for the canonical $4$-forms $Φ_{Spin(8)}$ and $Φ_{Spin(7)U(1)}$, associated with Clifford systems related with the subgroups $Spin(8)$ and $Spin(7)U(1)$ of $SO(16)$. We characterize the calibrated $4$-planes of the $4$-forms $Φ_{Spin(8)}$ and $Φ_{Spin(7)U(1)}$, extending in two different ways the notion of Cayley $4$-plane to dimension $16$.
A comparison among different constructions of the quaternionic $4$-form $Φ_{Sp(2)Sp(1)}$ and of the Cayley calibration $Φ_{Spin(7)}$ shows that one can start for them from the same collections of "Kähler 2-forms", entering in dimension 8 both in quaternion Kähler and in $Spin(7)$ geometry. This comparison relates with the notions of even Clifford structure and of Clifford system. Going to dimension $16$, similar constructions allow to write explicit formulas for the canonical $4$-forms $Φ_{Spin(8)}$ and $Φ_{Spin(7)U(1)}$, associated with Clifford systems related with the subgroups $Spin(8)$ and $Spin(7)U(1)$ of $SO(16)$. We characterize the calibrated $4$-planes of the $4$-forms $Φ_{Spin(8)}$ and $Φ_{Spin(7)U(1)}$, extending in two different ways the notion of Cayley $4$-plane to dimension $16$.
