Transgression forms in dimension 4
Abstract
We compute explicit transgression forms for the Euler and Pontrjagin classes of a Riemannian manifold of dimension 4 under a conformal change of the metric, or a change to a Riemannian connection with torsion. These formulae describe the singular set of some connections with singularities on compact manifolds as a residue formula in terms of a polynomial of invariants. We give some applications for minimal submanifolds of Kaehler manifolds. We also express the difference of the first Chern class of two almost complex structures, and in particular an obstruction to the existence of a homotopy between them, by a residue formula along the set of anti-complex points. Finally, we take the first steps in the study of obstructions for two almost quaternionic-Hermitian structures on a manifold of dimension 8 to have homotopic fundamental forms or isomorphic twistor spaces.
Cite
@article{arxiv.math/0412389,
title = {Transgression forms in dimension 4},
author = {Isabel M. C. Salavessa and Ana Pereira do Vale},
journal= {arXiv preprint arXiv:math/0412389},
year = {2007}
}
Comments
v1: 22 pages, plain LaTeX; v2: 25 pages: adds substancial results to v1, namely obstructions for two almost complex structures to be homotopic, obtaining residue formulas along anti-complex points, and obstructions for two fundamental forms of almost quaternionic- Hermitian structures to be homotopic. To appear in Int. J. Geom. Methods in Mod. Phys., special volume dedicated to D. Alekseevsky