论文标题
符号平坦的连接及其功能
Symplectically Flat Connections and Their Functionals
论文作者
论文摘要
我们继续研究符号扁平捆绑包。我们将符号歧管上的符号平坦连接的概念扩大到平滑歧管上的$ζ$ -FLAT连接。主束上的这些连接可以由从基地基本组扩展到结构组的地图表示。我们介绍零是符合性平坦连接并研究其关键点的功能。这样的功能导致新的几何流动。我们还描述了$ζ$ -FLAT捆绑包的一些特征类。
We continue our study of symplectically flat bundles. We broaden the notion of symplectically flat connections on symplectic manifolds to $ζ$-flat connections on smooth manifolds. These connections on principal bundles can be represented by maps from an extension of the base's fundamental group to the structure group. We introduce functionals with zeroes being symplectically flat connections and study their critical points. Such functionals lead to novel geometric flows. We also describe some characteristic classes of the $ζ$-flat bundles.
