Closed 3-forms in five dimensions and embedding problems
Differential Geometry
2022-10-31 v1
Abstract
We consider the question if a five dimensional manifold can be embedded into a Calabi-Yau manifold of complex dimension three such that the real part of the holomorphic volume form induces a given closed 3-form on the 5-manifold. We define an open set of 3-forms in dimension five which we call strongly pseudoconvex, and show that for closed strongly pseudoconvex 3-forms the perturbative version of this embedding problem can be solved if a finite dimensional vector space of obstructions vanishes.
Cite
@article{arxiv.2210.16208,
title = {Closed 3-forms in five dimensions and embedding problems},
author = {Simon Donaldson and Fabian Lehmann},
journal= {arXiv preprint arXiv:2210.16208},
year = {2022}
}