GL(2)-geometry and complex structures
Differential Geometry
2021-09-17 v1
Abstract
We study -structures on differential manifolds. The structures play a fundamental role in the geometric theory of ordinary differential equations. We prove that any -structure on an even dimensional manifold give rise to a certain almost-complex structure on a bundle over the original manifold. Further, we exploit a natural notion of integrability for the -structures, which is a counterpart of the self-duality for the 4-dimensional conformal structures. We relate the integrability of the -structures to the integrability of the almost-complex structures. This allows to perform a twistor-like construction for the -geometry. Moreover, we provide an explicit construction of a canonical connection for any -structure.
Cite
@article{arxiv.1910.12669,
title = {GL(2)-geometry and complex structures},
author = {Wojciech Kryński},
journal= {arXiv preprint arXiv:1910.12669},
year = {2021}
}