Transgression on hyperkähler manifolds and generalized higher torsion forms

• Anton Gerasimov ^[1] ; Alexei Kotov ^[2]
  1. [1] Institute for Theoretical and Experimental Physics
  2. [2] Campus Limpertsberg
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 12, Nº. 2, 2006, págs. 179-197
• Idioma: inglés
• DOI: 10.1007/s00029-006-0021-5
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• Resumen

  • We propose a generalization of the Hodge ddc-lemma to the case of hyperk¨ahler manifolds. As an application we derive a global construction of the fourth order transgression of the Chern character forms of hyperholomorphic bundles over compact hyperk¨ahler manifolds. In Section 3 we consider the fourth order transgression for the infinite-dimensional bundle arising from local families of hyperk¨ahler manifolds. We propose a local construction of the fourth order transgression of the Chern character form. We derive an explicit expression for the arising hypertorsion differential form. Its zero-degree part may be expressed in terms of the Laplace operators defined on the fibres of the local family.