Stable forms and special metrics
Differential Geometry
2007-05-23 v1
Abstract
We show how certain diffeomorphism-invariant functionals on differential forms in dimensions 6,7 and 8 generate in a natural way special geometrical structures in these dimensions: metrics of holonomy G2 and Spin(7), metrics with weak holonomy SU(3) and G2, and a new and unexplored example in dimension 8. The general formalism becomes a practical tool for calculating homogeneous or cohomogeneity one examples, and we illustrate this with some newly discovered cases of Spin(7) and G2 metrics.
Cite
@article{arxiv.math/0107101,
title = {Stable forms and special metrics},
author = {Nigel Hitchin},
journal= {arXiv preprint arXiv:math/0107101},
year = {2007}
}
Comments
Submitted to the ``Proceedings of the Congress in memory of Alfred Gray", (eds M. Fernandez and J. Wolf), AMS Contemporary Mathematics Series