近$G_2$流形的变形理论

IF 0.7 4区数学 Q2 MATHEMATICS

Communications in Analysis and Geometry Pub Date : 2024-01-04 DOI:10.4310/cag.2023.v31.n3.a5

Shubham Dwivedi, Ragini Singhal

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引用次数: 0

摘要

$def\G\{mathrm{G}_2}$我们研究近$\G$流形的变形理论。这些七维流形包含实基林旋量。我们证明近$\G$结构的无穷小变形一般是受阻的。我们明确地证明了阿洛夫-瓦拉几空间上同质近$\G$结构的无穷小变形都是二阶受阻的。我们还完整地描述了近$\G$流形的同调。

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Deformation theory of nearly $G_2$ manifolds

$\def\G{\mathrm{G}_2}$We study the deformation theory of nearly $\G$ manifolds. These are seven-dimensional manifolds admitting real Killing spinors. We show that the infinitesimal deformations of nearly $\G$ structures are obstructed in general. Explicitly, we prove that the infinitesimal deformations of the homogeneous nearly $\G$ structure on the Aloff–Wallach space are all obstructed to second order. We also completely describe the cohomology of nearly $\G$ manifolds.

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来源期刊

Communications in Analysis and Geometry 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes high-quality papers on subjects related to classical analysis, partial differential equations, algebraic geometry, differential geometry, and topology.