Harmonic Twistor Formalism and Transgression on Hyperkähler manifolds

Details Harmonic Twistor Formalism and Transgression on Hyperkähler manifolds Harmonic Twistor Formalism and Transgression on Hyperkähler manifolds

2000-12-26

arxiv.org/abs/math/0012249v1

J.Geom.Phys. 44 (2002) 41-51

Mathematics

Differential Geometry

10pp., Latex

Scientific paper

In this paper we continue our study of the fourth order transgression on hyper\"ahler 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 hyperk\"ahler 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 $\bar{\partial}$-operator defined on fibers of the twistor fibration.

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