Closed 3-forms in five dimensions and embedding problems

Simon Donaldson; Fabian Lehmann

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arXiv · 2210.16208

Closed 3-forms in five dimensions and embedding problems

Simon Donaldson·Fabian Lehmann

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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.

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Simon Donaldson, Fabian Lehmann. 2022-10-28. Closed 3-forms in five dimensions and embedding problems. https://arxiv.org/abs/2210.16208

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