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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2020, том 16, 027, 35 стр. (Mi sigma1564)

Эта публикация цитируется в 3 статьях

Bach Flow on Homogeneous Products

Dylan Helliwell

Department of Mathematics, Seattle University, 901 12th Ave, Seattle, WA 98122, USA

Аннотация: 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.

Ключевые слова: high-order geometric flows, Bach flow, locally homogeneous manifold, three-dimensional Lie group.

MSC: 53C44, 53C30, 34C40

Поступила: 3 сентября 2019 г.; в окончательном варианте 29 марта 2020 г.; опубликована 11 апреля 2020 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2020.027



Реферативные базы данных:
ArXiv: 1803.07733


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