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Harmonic twistor formalism and transgression on hyperkähler manifolds

✍ Scribed by A. Gerasimov; A. Kotov

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
92 KB
Volume
44
Category
Article
ISSN
0393-0440

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✦ Synopsis

In this paper we continue our study of the fourth-order transgression on hyperähler manifolds introduced in the previous paper. We give a local construction for the fourth-order transgression of the Chern character form of an arbitrary vector bundle supplied with a self-dual connection on a four-dimensional hyperkähler manifold. The construction is based on the harmonic twistor formalism. Remarkably, the resulted expression for the fourth-order transgression is given in terms of the determinant of the ∂-operator defined on fibers of the twistor fibration.

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Harmonic and holomorphic 1-forms on compact balanced Hermitian manifolds
✍ Georgi Ganchev; Stefan Ivanov 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 97 KB

On compact balanced Hermitian manifolds we obtain obstructions to the existence of harmonic 1-forms, ∂-harmonic (1, 0)-forms and holomorphic (1, 0)-forms in terms of the Ricci tensors with respect to the Riemannian curvature and the Hermitian curvature. Necessary and sufficient conditions the (1, 0)