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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2020 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2020
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210583 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Bach Flow on Homogeneous Products. Dylan Helliwell. SIGMA 16 (2020), 027, 35 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862618287539486720 |
|---|---|
| author | Helliwell, Dylan |
| author_facet | Helliwell, Dylan |
| citation_txt | Bach Flow on Homogeneous Products. Dylan Helliwell. SIGMA 16 (2020), 027, 35 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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׳ proves to be the most challenging and interesting.
|
| first_indexed | 2025-12-17T12:04:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210583 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:16Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| 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׳ 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 |
| spellingShingle | Bach Flow on Homogeneous Products Helliwell, Dylan |
| title | 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_short | Bach Flow on Homogeneous Products |
| title_sort | bach flow on homogeneous products |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210583 |
| work_keys_str_mv | AT helliwelldylan bachflowonhomogeneousproducts |