Hyperkähler流形上的超越与广义高阶挠型
Transgression on Hyperkähler Manifolds and Generalized Higher Torsion Forms
摘要：
本文将Hodge $dd_c$ -引理推广到超凯勒流形上.作为这个结果的应用，我们得到了紧致超kähler流形上超全纯丛的Chern特征标形式的四阶超越的整体构造.本文的第二部分考虑了由局部超Kähler流形族产生的无穷维丛的四阶超进。我们提出了一个局部构造的第四级海侵的陈特征标形式。给出了超挠微分形式的显式表示。它的零度部分可以用定义在局部族纤维上的拉普拉斯算子来表示。
英文摘要：
We propose a generalization of the Hodge $dd_c$-lemma to the case of hyperkähler manifolds. As an application of this result we derive the global construction of the fourth order transgression of the Chern character forms of hyperholomorphic bundles over compact hyperkähler manifolds. At the second part of the paper we consider the fourth order transgression for the infinite dimensional bundle arising from local families of hyperkähler manifolds. We propose a local construction of the fourth order transgression of the Chern character form. We derive an explicit expression for arising hypertorsion differential form. It's zero-degree part may be expressed in terms of the Laplace operators defined on the fibers of the local family.
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