Bach Flow on Homogeneous Products

The 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 equa...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2020
Автор: Helliwell, Dylan
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2020
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/210583
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Bach Flow on Homogeneous Products. Dylan Helliwell. SIGMA 16 (2020), 027, 35 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-210583
record_format dspace
spelling Helliwell, Dylan
2025-12-12T10:29:36Z
2020
Bach Flow on Homogeneous Products. Dylan Helliwell. SIGMA 16 (2020), 027, 35 pages
1815-0659
2020 Mathematics Subject Classification: 53C44; 53C30; 34C40
arXiv:1803.07733
https://nasplib.isofts.kiev.ua/handle/123456789/210583
https://doi.org/10.3842/SIGMA.2020.027
The 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. The limiting behavior of the metric and the curvature is determined in all cases. The behavior of quotients of ℝ×𝕊³ proves to be the most challenging and interesting.
The author would like to thank Eric Bahuaud for the many valuable discussions while developing this paper, and the referees for their in-depth, candid feedback and constructive suggestions for improvement.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Bach Flow on Homogeneous Products
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Bach Flow on Homogeneous Products
spellingShingle Bach Flow on Homogeneous Products
Helliwell, Dylan
title_short Bach Flow on Homogeneous Products
title_full Bach Flow on Homogeneous Products
title_fullStr Bach Flow on Homogeneous Products
title_full_unstemmed Bach Flow on Homogeneous Products
title_sort bach flow on homogeneous products
author Helliwell, Dylan
author_facet Helliwell, Dylan
publishDate 2020
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description The 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. The limiting behavior of the metric and the curvature is determined in all cases. The behavior of quotients of ℝ×𝕊³ proves to be the most challenging and interesting.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/210583
citation_txt Bach Flow on Homogeneous Products. Dylan Helliwell. SIGMA 16 (2020), 027, 35 pages
work_keys_str_mv AT helliwelldylan bachflowonhomogeneousproducts
first_indexed 2025-12-17T12:04:16Z
last_indexed 2025-12-17T12:04:16Z
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