2000/12/26 by A. Gerasimov, Gerasimov, A., A. Kotov +2
Mathematics · Medicine · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Neuroimaging Techniques and Applications #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #K-Theory and Homology (math.KT) #hep-th #math.DG #math.KT
paper · pdf · doi:10.48550/arxiv.math/0012248
17pp., Latex
arxiv created 2000/12/26 · openalex publication_date 2000/12/26 · arxiv updated 2009/11/30 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
We propose a generalization of the Hodge ddc-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.