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Mathematics > Differential Geometry

arXiv:1803.07733 (math)
[Submitted on 21 Mar 2018 (v1), last revised 16 Apr 2020 (this version, v3)]

Title:Bach Flow on Homogeneous Products

Authors:Dylan Helliwell
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Abstract:Qualitative behavior of Bach flow is established on compact four-dimensional locally homogeneous product manifolds. This is achieved by lifting to the homogeneous universal cover and, in most cases, capitalizing on the resultant group structure. The resulting system of ordinary differential equations is carefully analyzed on a case-by-case basis, with explicit solutions found in some cases. Limiting behavior of the metric and the curvature are determined in all cases. The behavior on quotients of $\mathbb{R} \times \mathbb{S}^3$ proves to be the most challenging and interesting.
Subjects: Differential Geometry (math.DG)
MSC classes: Primary: 53C44, Secondary: 53C30, 34C40
Cite as: arXiv:1803.07733 [math.DG]
  (or arXiv:1803.07733v3 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1803.07733
Journal reference: SIGMA 16 (2020), 027, 35 pages
Related DOI: https://doi.org/10.3842/SIGMA.2020.027

Submission history

From: Dylan Helliwell [view email]
[v1] Wed, 21 Mar 2018 03:40:27 UTC (207 KB)
[v2] Thu, 15 Aug 2019 01:20:12 UTC (206 KB)
[v3] Thu, 16 Apr 2020 03:25:45 UTC (209 KB)
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