Bach flow of simply connected nilmanifolds

IF 0.5 4区 数学 Q3 MATHEMATICS Advances in Geometry Pub Date : 2024-01-24 DOI:10.1515/advgeom-2023-0032
Adam Thompson
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Abstract

The Bach flow is a fourth-order geometric flow defined on four-manifolds. For a compact manifold, it is the negative gradient flow for the L 2-norm of the Weyl curvature. In this paper, we study the Bach flow on four-dimensional simply connected nilmanifolds whose Lie algebra is indecomposable. We show that the Bach flow beginning at an arbitrary left invariant metric exists for all positive times and after rescaling converges in the pointed Cheeger–Gromov sense to an expanding Bach soliton which is non-gradient. Combining our results with previous results of Helliwell gives a complete description of the Bach flow on simply connected nilmanifolds.
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简单连接无穷流的巴赫流
巴赫流是定义在四曲面上的四阶几何流。对于紧凑流形,它是韦尔曲率 L 2-norm 的负梯度流。在本文中,我们研究了四维简单连接零曼形上的巴赫流,这些零曼形的李代数是不可分解的。我们的研究表明,从任意左不变度量开始的巴赫流在所有正时间内都存在,并且在重定标后会在尖的切格-格罗莫夫意义上收敛到一个非梯度的膨胀巴赫孤子。将我们的结果与海利韦尔之前的结果结合起来,就能完整地描述简单相连无芒物上的巴赫流。
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来源期刊
Advances in Geometry
Advances in Geometry 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
31
审稿时长
>12 weeks
期刊介绍: Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.
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