辛平坦联络及其泛函
Symplectically Flat Connections and Their Functionals
摘要：
我们继续研究辛平坦丛。我们将辛流形上的辛平坦联络的概念推广到光滑流形上的$ζ$ -平坦联络。这些在主丛上的联系可以用从基底的基本群的扩张到结构群的映射来表示。引入零点为辛平坦联络的泛函并研究其临界点。这样的泛函导致新的几何流。我们还描述了$ζ$ -平坦丛的一些特征类。
英文摘要：
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.
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