Affiliation:
1. Department of Mathematics Imperial College London London UK
2. Humboldt‐Universität zu Berlin Institut für Mathematik Berlin Germany
Abstract
AbstractWe consider the question if a five‐dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 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.
Reference16 articles.
1. Einstein Manifolds
2. Studies in Advanced Mathematics;Boggess A.,1991
3. Intégration des équations Cauchy–Riemann induites formelles;Boutet de Monvel L.;Sémin. Équ. Dériv. Partielles (Polytechnique),1974
4. Generalized Killing spinors in dimension 5
5. An elliptic boundary value problem for $G_{2}$-structures