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https://hdl.handle.net/1959.11/26558
Title: | Ricci-positive geodesic flows and point-completion of static monopole fields | Contributor(s): | Dorji, Kumbu (author); Harris, Adam (author) | Publication Date: | 2019-05 | Early Online Version: | 2019-02-05 | DOI: | 10.1016/j.geomphys.2019.01.003 | Handle Link: | https://hdl.handle.net/1959.11/26558 | Abstract: | Let (Mˆ, g) be a compact, oriented Riemannian three-manifold corresponding to the metric point-completion M ∪{P₀} of a manifold M, and let ξ denote a geodesible Killing unit vector field on Mˆ such that the Ricci curvature function Ricg (ξ ) > 0 everywhere, and is constant outside a compact subset K ⊂⊂ M. Suppose further that (E, ∇, ϕ) supply the essential data of a monopole field on M, smooth outside isolated singularities all contained in K. The main theorem of this article provides a sufficient condition for smooth extension of (E, ∇, ϕ) across P₀, in terms of the Higgs potential Φ, defined in a punctured neighbourhood of P₀ by ∇ξΦ − 2i[ϕ, Φ] = ϕ . The sufficiency condition is expressed by a system of equations on the same neighbourhood, which can be effectively simplified in the case that Mˆ is a regular Sasaki manifold, such as the round S³. | Publication Type: | Journal Article | Source of Publication: | Journal of Geometry and Physics, v.139, p. 78-87 | Publisher: | Elsevier BV, North-Holland | Place of Publication: | Netherlands | ISSN: | 0393-0440 | Fields of Research (FoR) 2008: | 010102 Algebraic and Differential Geometry | Fields of Research (FoR) 2020: | 490402 Algebraic and differential geometry | Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | Socio-Economic Objective (SEO) 2020: | 280118 Expanding knowledge in the mathematical sciences | Peer Reviewed: | Yes | HERDC Category Description: | C1 Refereed Article in a Scholarly Journal |
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Appears in Collections: | Journal Article School of Science and Technology |
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