Closed 3-forms in five dimensions and embedding problems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-05 DOI:10.1112/jlms.12897

Simon Donaldson, Fabian Lehmann

引用次数: 0

Abstract

We 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.

Abstract Image

查看原文本刊更多论文

五维封闭三形式与嵌入问题

我们考虑的问题是，能否将一个五维流形嵌入到一个复维度为 3 的 Calabi-Yau 流形中，从而使全形体积形式的实部在五维流形上诱导出一个给定的封闭 3 形式。我们定义了一个五维 3 形的开放集合，称之为强伪凸，并证明了对于封闭的强伪凸 3 形，如果一个有限维的障碍向量空间消失，这个嵌入问题的扰动版本就可以求解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.